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Capacity and Congestion Due to Incidents at Freeway Facilities

Permanent Link: http://ufdc.ufl.edu/UFE0043612/00001

Material Information

Title: Capacity and Congestion Due to Incidents at Freeway Facilities
Physical Description: 1 online resource (196 p.)
Language: english
Creator: Lu, Cuie
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: incidents
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Incidents lower freeway capacity and increase delay, especially during high demand and oversaturated flow conditions. This dissertation investigates freeway capacity and congestion due to incidents through four aspects that are detailed below, based on data collected from five freeway facilities in North America. A qualitative analysis of the impact of incidents on operational conditions was first conducted by constructing time-series plots and density maps. It was determined that incidents which are verified to affect traffic flow are mostly collisions with durations greater than 10 minutes. Changes in flow, speed and occupancy at the beginning of congestion that was caused by incidents are much steeper than that at the beginning of recurrent (i.e., demand-induced) congestion. Generally, the speed of shockwaves for incident-induced breakdowns is larger than that for demand-induced breakdowns. Next, maximum throughput-related values were obtained to estimate capacity under non-incident conditions as well as under incident conditions. Under non-incident conditions, the data indicate that three-lane freeways are the most efficient in terms of per lane capacity. Two multiple linear regression models were developed to predicts the capacity of a section during incident conditions and capacity reduction during incidents. The results suggest that apart from the number of lanes affected by incidents, incident category and total number of lanes are significant in incident capacity estimation. The Product Limit Method (PLM) is reviewed and extended to estimate the probability of breakdown caused by incidents (defined as incident-induced breakdown) based on five different traffic parameters. The results show that flow is more appropriate than the other parameters in estimating the probability of breakdown. The results are also compared to the probability of demand-induced breakdown based on the same parameters, and found that at the same flow rate, the probability of incident-induced breakdown is higher than the probability of demand-induced breakdown. Finally, the dissertation investigates whether the incident occurrence (primarily crashes) can be detected based on likelihood of incident functions using the PLM. The analysis considers seven different traffic parameters. The likelihood functions of incident based on each parameter is first developed using the PLM for congested and non-congested conditions at each site. An incident detection index is then proposed based on the PLM results. The analysis results show that, at all the sites, four parameters are significant in incident detection: flow, occupancy, standardized speed difference, and 5-min average variation of speed. The proposed index is evaluated with detector data (both clean data and raw data), and compared to previously developed algorithms. The results show that the proposed index yields higher detection rate and lower mean detection time. The clean data generate fewer false alarms than the raw data. It is also found that most of the false alarms occur during congested conditions. The false alarm rate can be reduced by decreasing the index coefficients; however, the detection rate would also be reduced.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Cuie Lu.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Elefteriadou, Ageliki L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043612:00001

Permanent Link: http://ufdc.ufl.edu/UFE0043612/00001

Material Information

Title: Capacity and Congestion Due to Incidents at Freeway Facilities
Physical Description: 1 online resource (196 p.)
Language: english
Creator: Lu, Cuie
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: incidents
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Incidents lower freeway capacity and increase delay, especially during high demand and oversaturated flow conditions. This dissertation investigates freeway capacity and congestion due to incidents through four aspects that are detailed below, based on data collected from five freeway facilities in North America. A qualitative analysis of the impact of incidents on operational conditions was first conducted by constructing time-series plots and density maps. It was determined that incidents which are verified to affect traffic flow are mostly collisions with durations greater than 10 minutes. Changes in flow, speed and occupancy at the beginning of congestion that was caused by incidents are much steeper than that at the beginning of recurrent (i.e., demand-induced) congestion. Generally, the speed of shockwaves for incident-induced breakdowns is larger than that for demand-induced breakdowns. Next, maximum throughput-related values were obtained to estimate capacity under non-incident conditions as well as under incident conditions. Under non-incident conditions, the data indicate that three-lane freeways are the most efficient in terms of per lane capacity. Two multiple linear regression models were developed to predicts the capacity of a section during incident conditions and capacity reduction during incidents. The results suggest that apart from the number of lanes affected by incidents, incident category and total number of lanes are significant in incident capacity estimation. The Product Limit Method (PLM) is reviewed and extended to estimate the probability of breakdown caused by incidents (defined as incident-induced breakdown) based on five different traffic parameters. The results show that flow is more appropriate than the other parameters in estimating the probability of breakdown. The results are also compared to the probability of demand-induced breakdown based on the same parameters, and found that at the same flow rate, the probability of incident-induced breakdown is higher than the probability of demand-induced breakdown. Finally, the dissertation investigates whether the incident occurrence (primarily crashes) can be detected based on likelihood of incident functions using the PLM. The analysis considers seven different traffic parameters. The likelihood functions of incident based on each parameter is first developed using the PLM for congested and non-congested conditions at each site. An incident detection index is then proposed based on the PLM results. The analysis results show that, at all the sites, four parameters are significant in incident detection: flow, occupancy, standardized speed difference, and 5-min average variation of speed. The proposed index is evaluated with detector data (both clean data and raw data), and compared to previously developed algorithms. The results show that the proposed index yields higher detection rate and lower mean detection time. The clean data generate fewer false alarms than the raw data. It is also found that most of the false alarms occur during congested conditions. The false alarm rate can be reduced by decreasing the index coefficients; however, the detection rate would also be reduced.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Cuie Lu.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Elefteriadou, Ageliki L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043612:00001


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1 CAPACITY AND CONGESTION DUE TO INCIDENTS AT FREEWAY FACILITIES By CUIE LU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2011

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2 2011 Cuie Lu

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3 To my parents and my husband

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4 ACKNOWLEDGMENTS I am so happy that I have finished this dissertation, and am glad to thank a lot of people who have made this dissertation possible. I am heartily thankful to my advisor Dr. Lily Elefteriadou, for her patience, guidance, and support through these four years for her confidence in me in conducting research. Her rich knowledge and numerous great ideas have helped me overcome many difficulties in the dissertation. I am also thankful to her for carefully reading and commenting on all my writings I d like to thank my committee menders Dr. Panos Pardalos Dr. Scott Washburn, Dr. Sivaramakrishnan Srinivasan, and Dr. Yafeng Yin, for their very help ful insights and valuable suggestions to my dissertation. Thanks go out to Mr. Sampson. I have learned a lot in their classes. This dissertation was mainly based on data collected for the National Cooperative Highway Research Program ( NCHRP ) 3 87 project. I would like to acknowledge Dr. Alexandra Kondyli who was responsible for data collection under that project. My thank is also extended to David Tsui of the Ontario Ministry of Transportation (MTO) Professor Baher Abdulhai of University of Toronto, Rich Bailey of Oregon Department of Transportation (ODOT), Simon Foo at McMaster University in Canada, Professor Fred L. Hall of University of Calgary, for their generous help in providing the data. I am pleased to thank Coordinator of the Center for Multimodal Solutions for Congestion Mitigation (CMS) Ms. Ines Aviles Spadoni for help ing me take part in various conferences and activities. She is smiling all the time and brings others pleasures. I also want to thank all my student colleagues in transportation for their friendships and help in projects and research.

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5 I cannot finish this dissertation without the support and encouragement of my parents and my husba nd. My parents endless love and confidence in me have given me strength and courage in pursuing the doctoral degree. Thanks go to my husband, who encourages and supports me all the time. He share s my joys and gloom in both life and study. I am so lucky that I met him at this beautiful campus when I came here.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 9 LIST OF FIGURES ........................................................................................................ 11 ABSTRACT ................................................................................................................... 14 CHAPTER 1 INTRODUCTION .................................................................................................... 16 Background ............................................................................................................. 16 Objectives ............................................................................................................... 18 Overview of Methodology ....................................................................................... 19 Organization of Dissertation .................................................................................... 21 2 LITERATURE REVIEW .......................................................................................... 22 Definition and Measurement of Freeway Capacity ................................................. 22 Definition of Capacity in the Highway Capacity Manual (HCM) ........................ 22 Definition of Capacity in Other Research .......................................................... 25 Measurement of Capacity ................................................................................. 29 Summary .......................................................................................................... 33 The Process of Breakdown and Breakdown Models .............................................. 34 Freeway Capacity and Operation under Incident Conditions .................................. 37 Impact of Incidents on Freeway Capacity ......................................................... 38 Relationship between Incidents and Freeway Operations ................................ 41 Summary .......................................................................................................... 45 Identification and Verification of Incidents ............................................................... 46 Incident Detection ............................................................................................. 46 Incident Prediction ............................................................................................ 50 Incident Verification .......................................................................................... 57 Summary .......................................................................................................... 59 Ramp Management Strategies Responsive to Incidents ........................................ 60 Ramp Closure .................................................................................................. 61 Ramp Metering ................................................................................................. 62 Summary .......................................................................................................... 64 3 DATA COLLECTION AND METHODOLOGY ......................................................... 78 Database Overview ................................................................................................ 78 Type of Data ..................................................................................................... 78 Site Descriptions .............................................................................................. 79

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7 Methodolog y ........................................................................................................... 82 Data Screening ................................................................................................. 82 Incident Verification .......................................................................................... 84 Data Analysis Procedure .................................................................................. 86 Database Overview .......................................................................................... 87 4 QUALITAT IVE ANALYSIS OF THE IMPACTS OF INCIDENTS ON OPERATIONAL CONDITIONS ............................................................................... 92 Time series Plots .................................................................................................... 92 Density Maps .......................................................................................................... 98 Conclusions .......................................................................................................... 102 5 FREEWAY CAPACITY UNDER INCIDENT CONDITIONS .................................. 117 C apacity under N onincident C onditions ............................................................... 117 C apacity for I ncident C onditions ........................................................................... 119 Capacity under Incident Conditions ................................................................ 119 Estimate of Capacity/Capacity Reduction under Incident Conditions ............. 123 C onclusions and R ecommendations .................................................................... 125 6 AN INVESTIGATION OF THE PROBABILITY OF BREAKDOWN AND INCIDENT INDUCED BREAKDOWN AT FREEWAYS ........................................ 133 Overview of the Product Limit Method (PLM) ....................................................... 134 Application of the Product Limit Method for Incident Conditions ........................... 137 Probability of D emand induced B reakdown .......................................................... 138 Description of D ata and A nalysis P rocedure .................................................. 139 Demandinduced B reakdown M odels ............................................................. 139 Flow based model .................................................................................... 139 Occupancy based model ......................................................................... 140 Speed differencebased model ................................................................ 142 5 min standard deviation of speedbased model ..................................... 143 5 min average variation of speedbased model ....................................... 143 Probability of I ncident induced B reakdown ........................................................... 144 Process for I nvestigating the P robability of I ncident induced B reakdown ...... 145 Incident induced B reakdown M odels .............................................................. 145 Comparison of D emand induced and I ncident induced B reakdown M odels ......... 147 Conclu sions .......................................................................................................... 148 7 FREEWAY INCIDENT DETECTION USING LIKELIHOOD OF INCIDENT FUNCTIONS ......................................................................................................... 158 Methodology ......................................................................................................... 159 Description of D ata ......................................................................................... 160 Definition of P arameters and Traffic States .................................................... 160 Calculation of the PLM ................................................................................... 161 Resu lts of the PLM and Incident Detection Index ................................................. 162

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8 PLM for Non congested C onditions ................................................................ 162 PLM for Congested C onditions ....................................................................... 163 Proposed Index of Incident Detection ............................................................. 163 Model Evaluation and Comparison to Previous Research .................................... 165 Concluding Remarks ............................................................................................. 169 8 FUTURE WORK ................................................................................................... 180 APPENDIX A FOR MAT OF DATA .............................................................................................. 182 LIST OF REFERENCES ............................................................................................. 186 BIOGRAPHICAL SKETCH .......................................................................................... 196

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9 LIST OF TABLES Table page 2 1 Summary of the l iterature on capacity d efinition ................................................. 66 2 2 Portion of freeway capacity available under incident conditions ......................... 67 2 3 Probability of lane closure due to crashes and breakdowns ............................... 67 2 4 Probability distribution of number of lanes closed ............................................... 67 2 5 Capacity remaining after incidents (nonincident capacity = 1.000) .................... 68 2 6 Percent of freeway capacity available under incident conditions ........................ 68 2 7 Performance of some common incident detection algorithms ............................ 69 2 8 Estimated binary logit model for collision incident .............................................. 69 2 9 Summary of research on incident detection ....................................................... 70 2 10 Summary of research on incident prediction ...................................................... 71 3 1 Description of data available .............................................................................. 88 3 2 Summary of data analysis .................................................................................. 88 4 1 Relationship between incidents and beginning of congestion .......................... 103 4 2 Changes in operational conditions 5min before/after breakdown or 5min before/afte r incidents ........................................................................................ 103 4 3 Operational conditions during different states at each data collection sites.. .... 104 4 4 Changes in density at the beginning of congestion or incidents at Toronto site 104 5 1 Capacity estimates for nonincident conditions ................................................. 127 5 2 Incident capac ity and number of lanes affected ............................................... 128 5 3 Comparison of incident capacity at different sites ............................................. 128 5 4 Comparison of percent of freeway capacity available under incident conditions ......................................................................................................... 129 5 5 Effects of v arious factors on parameters of incident capacity ........................... 130

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10 5 6 Estimates of parameters for regression to estimate the minimum 10min flow rate ................................................................................................................... 130 5 7 Estimates of parameters for regression to estimate the total capacity reduction ........................................................................................................... 131 6 1 Summary of site characteristics and data available .......................................... 151 7 1 Overview of site characteristics and data ......................................................... 171 7 2 Relationship between likelihood of incident and each parameter for noncongested conditions ........................................................................................ 171 7 3 Relationship between likelihood of incident and each parameter for congest ed conditions ........................................................................................ 171 7 4 Characteristics of evaluation data and evaluation results ................................. 172 7 5 Comparison results of the proposed index to previous algorithm s ................... 172 A 1 Format of data at I 15 SB ................................................................................. 184 A 2 Format of data at I 5 NB ................................................................................... 184 A 3 Format of data at the Queen Elizabeth Way (QEW) site .................................. 184 A 4 Format of data at the US 217 SB ...................................................................... 185 A 5 Format of data at the US 494 EB ...................................................................... 185

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11 LIST OF FIGURES Figure page 1 1 Flow chart of the dissertation .............................................................................. 21 2 1 Illustration of three parameters on timeseries plot of flow and speed ................ 72 2 2 Probability of F S transition and the corresponding capacity .............................. 72 2 3 Capacity distributions for a 3lane freeway with and without variable speed control (13.5% average truck percentage, 5minute interval) ............................. 73 2 4 Probability of breakdowns in 15 min by Elefteriadou et al., reproduced ............. 73 2 5 Probability of breakdown versus observed flow rate Site A ........................... 74 2 6 R elationship between incident types and number of lanes affected ................... 74 2 7 Relationship between v/c and accident rate at basic freeway section ................ 75 2 8 Structure of basic California incident detection algorithm ................................... 75 2 9 Predicted collision likelihood ............................................................................... 76 2 10 Example of i ncident o ccupancy .......................................................................... 76 2 11 Incident caused o ccupancy at m ultiple s tations .................................................. 77 3 1 Location of detectors at I 15 SB ......................................................................... 89 3 2 Location of detectors at I 5 NB ........................................................................... 89 3 3 Schematic of detectors at the Queen Elizabeth Way (QEW) Site ....................... 89 3 4 Location of detectors at QEW ............................................................................. 90 3 5 Schematic of the Portland site ............................................................................ 90 3 6 Location of detectors at the Portland site ........................................................... 90 3 7 Location of detectors at the Minneapolis site ...................................................... 91 3 8 Verification of incident on Jan 28, 2005 .............................................................. 91 4 1 Time series speed and flow plots for condition with no i ncident. ...................... 105 4 2 Time series plots for incidents occurring before breakdown (March 9, 2005) ... 106

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12 4 3 Time series plots for incident during the congested period (Oct 6, 2005) ......... 107 4 4 Time series plots for incident occurring downstream condition (Sep 19, 2005) 108 4 5 Time series speed and flow plots for minor incidents (Nov 8, 2005) ................. 109 4 6 Distributions of the changes in operations for no incident and incident conditions ........................................................................................................ 110 4 7 Density map of Feb 10 2005 without incident ................................................... 111 4 8 Density map of March 9 2005 with incident at 17:1718:01 at 490DES ............ 112 4 9 Density map of May 25 2005 with incident at 9:5710:27 at 440DES ............... 113 4 10 Density map of Oct 6 2005 with incident at 8:028:38 at 440DES (5min) ........ 114 4 11 Density map of Oct 6 2005 with incident at 8:028:38 at 440DES (1min) ........ 115 4 12 Density Map of Sep 22 2005 with Incident at 17:1619:46 at 510DES ............. 116 5 1 Ca pacity parameters by number of lanes ......................................................... 132 6 1 Probability of demandinduced breakdown based on flow ................................ 152 6 2 Probability of demandinduced breakdown based on occupancy ..................... 152 6 3 Probability of demandinduced breakdown at the two bottleneck locations at Toronto site....................................................................................................... 153 6 4 Probability of demandinduced breakdown based on normalized speed difference .......................................................................................................... 154 6 5 Probability of demandinduced breakdown based on 5min std.v ..................... 154 6 6 Probability of demandinduced breakdown based on 5min cvs ....................... 155 6 7 Probability of incid ent induced breakdown. ...................................................... 156 6 8 Comparison of probabilities of demandinduced breakdown and incident induced breakdown. ......................................................................................... 157 7 1 Likelihood of incident for noncongested conditions. ........................................ 173 7 2 Likelihood of incident for congested conditions ................................................ 174 7 3 Likelihood of incident potential based on each parameter for incidents occurring before congestion ............................................................................. 175

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13 7 4 Likelihood of incident potential based on each parameter for incidents occurring during congestion .............................................................................. 176 7 5 Evaluation results of incident detection ............................................................ 179

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14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CAPACITY AND CONGESTION DUE TO INCIDENTS AT FREEWAY FACILITIES By Cuie Lu December 2011 Chair: Lily Elefter ia dou Major: Civil Engineering Incidents lower freeway capacity and increase delay, especially during high demand and oversaturated flow conditions. Th is dissertation investigates freeway capacity and congestion due to incidents through four aspects that are detailed below based on dat a collected from five freeway facilities in North America. A qualitative analysis of the impact of incidents on operational conditions was first conducted by constructing time series plots and density maps. It wa s determine d that incidents which are verifi ed to affect traffic flow are mostly collisions with durations greater than 10 minutes. C hanges in flow, speed and occupancy at the beginning of congestion that was caused by incidents are much steeper than that at the beginning of recurrent (i.e., demand induced) congestion. Generally, the speed of shockwaves for incident induced breakdowns is larger than that for demand induced breakdowns. Next, m aximum throughput related values were obtained to estimate capacity under no n incident conditio ns as well as under incident conditions. Under non incident conditions, the data indicate that three lane freeway s are the most efficient in terms of per lane capacity T wo multiple linear regression model s were developed to predicts the capacity of a sect ion during incident conditions and capacity reduction during incidents.

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15 The results suggest that apart from the number of lanes affected by incidents, incident category and total number of lanes are significant in incident capacity estimation T he Product Limit Method (PLM) is reviewed and extended to estimate the probability of breakdown caused by incidents (defined as incident induced breakdown) based on five different traffic parameters. The results show that flow is more appropriate than the other parameters in estimating the probability of breakdown. The results are also compared to the probability of demandinduced breakdown based on the same parameters and found that at the same flow rate, the probability of incident induced breakdown is higher than the probability of demandinduced breakdown. Finally, the dissertation investigates whether the incident occurrence (primarily crashes) can be detected based on likelihood of incident functions using the PLM The analysis considers sev en different traffic parameters. The likelihood functions of incident based on each parameter is first developed using the PLM for congested and noncongested conditions at each site. An incident detection index is then proposed based on the PLM results. The analysis results show that at all the sites, four parameters are significant in incident detection: flow, occupancy, standardized speed difference, and 5min average variation of speed. The proposed index is evaluated with detector data (both clean data and raw data) and compared to previously developed algorithm s. The results show that the proposed index yields high er detection rate and low er mean detect ion time. T he c lean data generate fewer false alarms than the raw data. It is also found that most of the false alarms occur during congested conditions. The false alarm rate can be reduced by decrea sing the index coefficients ; h owever, the detection rate would also be reduced.

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16 CHAPTER 1 I NTRODUCTION Background Freeway incidents are nonrecurring unexpected events that might disrupt traffic flow. These events include crashes, vehicle breakdowns, etc, which lead to delays, waste d fuel and lost productivity. According to Farradyne (2000), 70% of all incidents are reported, among which 80% are disabled vehicles 10% are crashes and 10% are other types of incidents According to their study, among the crashes 60% occur on the shoulder with a duration of 45 60 minutes and 40% block lanes with a duration of 45 90 minutes. Among the others, 70% occur on the shoulder with a duration of 15 30 minutes and 30% block lanes with a duration of 30 45 minutes. I ncidents account for approximately 60% of all urban freeways delay in US (Federal Highway Administration, 2000). At low and medium traffic demand conditions, incidents may lower the travel speed at the incident location and thus increase delay. The impact of incidents during high demand and oversaturated freeway flow conditions is much larger than that during low and medium traffic demand conditions due to two reasons. First, as indicated by Persaud and Azbik (1993), in cident s are more likely to occur during congested operations than during uncongested operation s at similar flows on the same highway. Second, traffic flow at higher density is relatively unstable and thus more easily affected by other disruptions such as incidents. Therefore, studying the impacts of incidents on freeway operation for high demand and oversaturated conditions is very impor tant for freeway operation efficiency and safety.

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17 In cident s may lead to capacity reduction, as they can block one or more lanes and/or the adjacent shoulder Previous research, such as the Highway Capacity Manual ( HCM 201 0) and that by Goolsby (1971), est imated the capacity during an incident based on the number of lanes closed by the incident, and report ed this capacity reduction as a deterministic value. However, there is no clear relationship between freeway capacity and other incident characteristics ( e.g., incident duration), or between freeway capacity and geometric characteristics. Nor is there estimated capacity during an incident based on a large dataset. Moreover, it is not clear whether the capacity value during an incident is a constant. Therefore, it is necessary to estimate capacity for incident conditions based on some other incident characteristics and geometric conditions, all of which are based on a larger dataset. This could help estimate capacity during incidents more accurately. The brea kdown of flow on freeway s is usually defined as the beginning of congestion. It describes the transition from relatively freef lowing traffic at speeds in the vicinity of the speed limit, to congestion, usually defined as stopand go traffic While several breakdown models have been proposed, such as the probabilistic model by Elefter ia dou et al (1995) and the model based on Markov process by Evans et al. (2001), there is limited research on the phenomenon of freeway breakdown induced by incident which wi ll be defined as incident induced breakdown in this dissertation. When an incident occur s, the freeway capacity at that section may be reduced, and vehicles may accumulate upstream The mechanism of the transition stage in which flow is changed from uncongested conditions to congested conditions when an incident occurs

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18 is not clear. It is also unknown whether an incident induced breakdown model could be developed. Thus, further research is deserved in these areas. With respect to the impact s of incidents on freeway operation, various incident management programs have been proposed and developed. Incident detection is a crucial step in incident management. Prompt and reliable incident detection is vital in reducing incident congestion and secondary incidents. However, existing incident detection algorithms do not consider many variables and have difficulty in differentiating incidents from congestion. Previous research has shown that r amp metering has the potential to delay or prevent breakdown (Elefteriadou et al., 200 9 ), and also the flexibility to be responsive during the incidents by updating the capacity value (Chang et al. 1994, Bogenberger et al. 2001). However, no incident pro bability model is used in those ramp metering algorithms. This dissertation reports the results of the study on the impact of incidents on freeway flow from three aspects: impact on operational conditions, impact on capacity, and impact on congestion, and propose some recommendations such as ramp metering in response to incidents Objectives The objectives of this dissertation are specified below. Conduct a qualitative analysis of the impacts of incidents on operations. The effects of incidents on operati ons will be studied by comparing flow, speed and occupancy as well as their variances before, during and after the incidents. The characteristics of breakdown and incident induced breakdown will also be compared. This would provide general information about the effects of incidents on freeway capacity, breakdown patterns, and incident detection Estimate freeway capacity under incident conditions. The relationship between capacity and incident characteristics, as well as the variability of capacity during different incident conditions, will be explored. The result s of this research may be incorporated into the HCM to provide a more accurate estimation of capacity for

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19 different incident conditions. They can also be used in incident management program s and ramp metering strateg ies to improve throughput and safety under incident conditions. Moreover, the result s can be appl ied to planning models to take into consideration various incident scenario s. I nvestigate the probability of incident induced break down The potential of d eveloping a probabilistic model of incident induced breakdown will be investigated, based on previous research on breakdown and field data analysis of traffic flow during incident s. Such a model could be used in traffic management a nd operations of freeway facilities (for example in ramp metering and variable speed limit algorithms.) Investigate the relationship between incident probability and operational conditions This objective is based on the observation that operational condi tions are distinct under non incident and various incident conditions. Such a relationship can be incorporated into ramp metering and other freeway management tools, to increase throughput and decrease delay on the freeway. The flow chart of this dissertation is described in Figure 11. O verview of Methodology This dissertation focuses on exploring the relationship between incidents, capacity, and breakdown. T o achieve these goals, previous research was reviewed, and the approach defined for this dissertat ion was developed considering these findings. The analysis will be based on a large dataset, which includes traffic data, incident data, weather data and geometric data that were collected from several freeway sections in North America. Based on the dataset, the following tasks were completed t o achieve each of the four objectives in this dissertation: Task 1: Literature Review. Previous research related to the definition and measurements of freeway capacity under various conditions, the process and models of flow breakdown, the impact of incidents on freeway operation and capacity incident verification and identification, as well as ramp metering strateg ies responsive to incidents are reviewed.

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20 Task 2: Data Assembly. The data used are based on the Nationa l Cooperative Highway Research Program ( NCHRP ) 3 87 project (Elefteriadou et al., 2009 ) Traffic data, weather data, incident data, and geometric data collected from five freeway sections for the project are used in this dissertation. Additional data are c ollected later. Task 3 : Data Analysis The data are firstly screened by weather and incident conditions. Only data with good weather conditions are kept for further analysis. Then incidents were verified by time, location, and effect and further separated into different groups according to the time and location of incidents as well as the time of congestion. Based on the analysis and literature review, an analysis method to achieve the objectives was developed. Task 4 : Explore the Relationship between Inci dents and Operational Conditions The relationships between incidents and beginning of congestion are investigated through time series plots and density maps. Operational conditions such as flow, speed and occupancy as well as their changes before, during and after the incidents are also obtained. This provides general information about the effects of incidents on freeway capacity, congestion, and incident prediction. Task 5 : Defin e and Measure Freeway Capacity for Incident Conditions. Based on the data analysis result s, a definition of freeway capacity for incident conditions is proposed and a method to measure the capacity for incident conditions is specified. Task 6 : Investigate the Relationship between Incident induced Breakdown Probability and Inciden ts. The potential of developing a probabilistic model of incident induced breakdown is investigated, and t he product limit method is considered and used in developing the model

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21 Task 7 : Detect Incidents as a Function of Operational Conditions. The relationship between incident probability and operational conditions is studied through the product limit method. Organization of Dissertation The second chapter reviews previous literature and provides conclusions on the definition and measurement of capacity, t he process and models of breakdown, the impact of incident s on freeway operation and capacity, incident identification and verification, and ramp management strategies responsive to incident s. The third chapter overviews the database and describes the methodology The fourth chapter qualitatively analyzes the impacts of incidents on operational conditions. The fifth chapter estimates freeway capacity for both nonincident and incident conditions. The sixth chapter investigates the potential of developing an incident induced breakdown probability model. The seventh chapter investigates the relationship between operational conditions and incident occurrence The last chapter concludes the dissertation and presents recommendations Field Data Impact of Incidents Impact on capacity Impact on probability of breakdown Impact on incident detection Freeway Management Incident management Ramp metering Variable speed limit Figure 1 1 Flow chart of the dissertation

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22 CHAPTER 2 L ITERATURE REVIEW This chapter reviews previous research related to freeway capacity, flow breakdown and incidents. The contents include the definition and measurement of capacity the process and models of flow breakdown, the impact s of incidents on freeway operations and capacity incident identification and verification, as well as ramp metering strateg ies responsive to incidents. Definition and Measurement of Freeway Capacity A main domain in incident research is capacity. The t erm Capacity is used to quantify the traffic carrying ability of transportation facilities. The capacity value is used in designing or rehabilitating highway facilities It is also used in evaluating whether an existing facility can satisfy the expected traffic demand. The definition and measurement of freeway capacity have been studied extensively, yet no agreement has been achieved. This section reviews literature related to the definition and measurement of freeway capacity for different traffic conditions. D efinition of C apacity in the Highway Capacity Manual ( HCM ) Originally published in 1950, the HCM was the first and most often used document to quantify the concept of capacity for transportation facilities. The HCM 1950 (HCM, 1950) defined three levels of roadway capacity : basic capacity, possible capacity and practical capacity. Basic capacity wa s the maximum number of passenger cars that can pass a point on a lane or roadway during one hour under the most nearly ideal roadway and traffic conditions which can possibly be attained. Possible capacity wa s the maximum number of vehicles that can pass a point on a lane or roadway during one hour under prevailing roadway and traffic

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23 conditions. Practical capacity wa s a lower selected volume that is meant to avoid high traffic density and improve drivers freedom of maneuver. Am ong the three definitions, the possible capacity was more similar to the definition used today with the exception that it didn t consider control conditions. It had also realized the variability of capacity by considering the roadway and traffic conditions, which may vary, in the definition. The practical capacity was related to the level of service concept and the service volume that corresponding to a specific LOS. The HCM 1965 (HCM, 1965) defined capacity as the maximum number of vehicles which had a reasonable expectation of passing over a given section of a lane or roadway in one direction (or in two lane direction for a twolane or threelane highway) during a given time period under prevailing roadway and traffic conditions, similarly to the pos sible capacity definition of the HCM 1950. This edition of the manual changed basic capacity to be capacity under ideal conditions and replaced practical capacity to be service volume under a series of conditions. The HCM 1985 (HCM, 1985) defined the capacity of a facility as the maximum hourly flow rate at which persons or vehicles reasonably can be expected to traverse a point or a uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions. I t stresse d that capacity refers to a rate of vehicular or person flow during a specified period of interest, which wa s most often a 15mintue period. This definition recognize d th e potential for substantial variations in flow during an hour, and f ocused analysis on intervals of maximum flow. The HCM 2000 (HCM, 2000) defined the capacity of a facility as the maximum hourly rate at which persons or vehicles reasonably can be expected to traverse a point

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24 or a uniform section of a lane or roadway duri ng a given time period under prevailing roadway, traffic, and control conditions. However, it still defined capacity as a deterministic value, although i t state d that capacity wa s not the absolute maximum flow rate observed on such a facility as d river ch aracteristics vary from region to region, and thus the absolute maximum flow rate can vary from day to day and from location to location. The HCM 20 1 0 (HCM, 20 1 0) defines the capacity of a freeway facility as the capacity of the critical segment (breakdown first) among those segments composing the default facility. It indicates that it is important to evaluate the individual segment demands and capacity. For a long time, traffic engineers have realized the inadequacy of the capacity definition mainly for two reasons ( Elefteriadou 2004) : firstly, the expression maximum hourly ratethat can reasonably be expected to... wa s not specific enough to obtain an estimate of capacity from field data, secondly, many previous research studi es ha d shown that the maximum throughput varies from day to day and from location to location. Additionally, the HCM 2000 state d that the turbulence due to merging and diverging maneuvers does not affect the capacity of the roadways invol ved. However, observations show that capacit ies at different links are different ( Jia et al 2 001). Therefore, there is a desire to define capacity under different conditions. The latest HCM pointed out this issue and suggested that freeway capacity shoul d be measured at the critical segment ( bottleneck ) In summary, the definition of capacity within the HCM has evolved overtime, and the capacity value provided by it has increased over time from 2000 pc/hr/ln to 2400

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25 pc/hr/ln for a basic freeway segment. T here has been a suggestion to consider the variability of maximum volumes in the capacity definition. Defini tion of C apacity in Other Research In parallel to the HCM, there have been other research efforts that study on the definition of capacity. The following reviews references related to the definition of capacity in other studies, especially capacity at freeway bottlenecks which is defined as the freeway segment after the merge point here, that is, the end of the acceleration lane. Agymang Duah and H all (1991) plotted the maximum prequeue flows and mean queue discharge flows in 15minute intervals and found the two distributions are similar. Based on the mean values of the two observed flows they recommended 2300 pc/h/ln as the capacity under stabl e flow conditions and 2200 pc/h/ln for the post breakdown conditions. However, the effect of site characteristics on capacity wa s not considered in their study Similarly, Persaud and Hurdle (1991) suggested the mean discharge flow as the most appropriate way to define capacity. This conclusion wa s drawn partly due to the consistency the researchers observed in its day to day measurement. Minderhoud et al. (1997) researched empirical capacity estimation methods for uninterrupted flow facilities and recommended the product limit method. According to the method, noncongested flow data were used to estimate the capacity distribution. However, this paper did not discuss the measurement of discharge flow. Cassidy and Bertini (1999) analyzed data from two freeway bottlenecks in Toronto, Canada. They observed lower discharge flow s than the flow s measured prior to the queue formation, and found that the discharge flow rates remain consistent from day to day while the maximum prequeue flows were generally unstable d uring short periods.

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26 Thus the authors suggested using the long run queue discharge flow as the bottleneck capacity, due to its reproducibility. However, defining the reproducible discharge flow as capacity somewhat ignores the random nature of capacity F reeway capacity is also related to flow breakdown, which is t he transition between proper operation and nonacceptable flow conditions Lorenz and Elefteriadou (2001) observed that flow rates may remain constant or even increase after breakdown, and that the flow drop after breakdown might be contingent upon the particular flow rate at which the facility break s down. Thus they suggested that a probability component should be incorporated into the freeway capacity definition. The proposed freeway capacity was the rate of flow (in pcphpl for a specified time interval) corresponding to the expected probability of breakdown under prevailing conditions. However, this paper d id not discuss maximum prebreakdown flow nor did it compare the breakdown flows to maxi mum discharge flows for each observation day. Elefteriadou and Lertworawanich (2003) defined and examined three flow parameters: the breakdown flow, the maximum prebreakdown flow, and the maximum discharge flow, based on freeway traffic data at two sites over a period of several days. The breakdown flow was defined as the 5min flow (or 15min flow) immediately prior to the breakdown event. The maximum prebreakdown flow was the maximum flow observed prior to the occurrence of congestion. And the maximum discharge flow wa s the maximum flow observed after the breakdown occurrence and prior to the recovery to noncongested conditions. Figure 21 illustrates th ese terms The authors concluded that the three parameters var y on a relatively large range and follow the normal distribution and that t he value of breakdown flow is almost always lower than both the

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27 maximum pre breakdown flow and the maximum discharge flow Moreover, they found that the maximum prebreakdown flow tends to be higher than the maximum discharge flow at one site but the opposite occurs at the other site and attributed this difference to geometric characteristics and sight distance. However, there is no detailed relationship provided between geometric characteristics and capacity estim ated Kerner (2004) stated that capacity at a bottleneck wa s determined by the transition from free flow to synchronized flow and is random by nature. The probability of transition depends on the traffic demand and on the time interval of the observations thus, there wa s an infinite number of freeway capacities in free flow at bottlenecks. The probability of transition from free flow to synchronized flow and the corresponding capacity at a bottleneck for a specific site are illustrated in Figure 22. Corresponding to Figure 22 the capacity of the freeway increased with increasing breakdown probability: the minimum capacity happens when the breakdown probability is 0 and the maximum capacity happens when the breakdown probability is 1. He also stated that along a homogeneous road the freeway capacity depends on which phase the traffic is in and thus defined maximum freeway capacities in free flow, in synchronized flow (all vehicles in the same direction have the same timeindependent speed) and in wide mov ing jams (congestion propagates upstream through bottleneck with a characteristic speed of about 16 km/h) The freeway capacity in free flow phase wa s the flow at which the transition from free flow to synchronized flow occurs; The capacity in synchronized flow wa s the maximum possible flow rate; The capacity at wide moving jams wa s equal to the flow rate in the wide moving jam outflow In conclusion, the author defined capacity at different locations and traffic states and treated it as a

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28 variable, similar to that proposed by Lorenz and Elefteriadou (2001), Persaud and Hurdle (1991). However, the reasons of the definitions were not fully explained. Brilon (2005) concluded from extensive data analysis that capacity is a variable, even under identical environmental conditions and considered only the volumes that cause the breakdown as capacities. This implies that capacity may not be the highest volume available. Similarly, Brilon et al. (2005) proposed that capacity should be understood as the traffic volume below which traffic still flows and above which the flow breaks down into stopandgo or even completely stop traffic. They estimated capacity using the Product Limit Method based on the statistics of lifetime data analysis and found that the capacity of a freeway section is Weibull distributed, h owever, different freeways m ight have different parameters. The estimated capacity distribution is shown in Figure 23 It can be seen from Figure 2 3 that capacity of the freeway increases with increasing breakdown probability, similar to the conclusion of Kerner (2004). C orresponding to a certain breakdown probability, the capacity of the section with variable speed limit is much higher than that without speed limit. Banks (2006) used average time gaps (average time separations between the rear of a vehicle and the front of a vehicle following it), average passage times (average times for vehicles to pass a point), and lane flow distributions as variables to link geometric, vehicle pop ulation, and driver population characteristics to capacity flows. Two types of capacity condition pre queue flow and queue discharge flow were considered. One major finding wa s that average time gaps appear ed to be the most important flow characteris tic for explaining variations in prequeue flow and queue discharge flow, and average passage times, on the other hand, were not correlated with

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29 flows. Finally, there wa s a strong, near linear negative relationship between critical lane flows and critical lane average time gaps in both prequeue and queue discharge flow. Yeon et al. (2007) proposed four parameters to define capacity, which wer e maximum pre breakdown flow, breakdown flow, maximum queue discharge flow and average queue discharge flow. They c oncluded from statistic analysis of speed and volume data that the average capacity flows during the AM peak period we re slightly higher than that during the PM peak period, and that capacity flows for both peak periods we re higher than those during nonpe ak periods. Among the four parameters of capacity, the average maximum prebreakdown flows at all the locations were the highest, while the average queue discharge flow s were the lowest. Literature related to the definition of capacity in other research is summarize d in Table 21 In summary, field data had shown that there wa s variability in the maximum flow observed, in the range of several hundred vehicles per hour per lane. Four different flow parameters (maximum prebreakdown flow, breakdown flow, maxi mum discharge flow and average queue discharge flow) were used to define the capacity of a freeway facility. The parameters m ight vary widely even at the same site, probably due to the microscopic characteristics of traffic and drivers such as individual spacing, time headway, speed of individual vehicles in traffic stream and their variabili ty However, there is limited research on a quantitative explanation of the flow variance and on the impact of site characteristics on the maximum flow distribution form. Measurement of Capacity C ritical issues for measuring capacity include the measurement location, the measurement time and the presence or absence of queues both upstream and

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30 downstream of the measurement location (Tian et al., 2005). This subsection reviews literature related to the time, location, and method of capacity measurement as well as the two capacity hypothesis Many researchers studied on the time and location of capacity measurement. Hall and Agyemang Duah (1991) stated that the queuedis charge capacity must be measured at an active bottleneck location, which wa s characterized by the presence of an upstream queue and the absence of a downstream queue, and that freeflow capacity measurement should be restricted to the period prior to break down when demand wa s approaching a maximum. For bottlenecks related to merge sections, the flow measurement location should be somewhere downstream of the freeway merge, so that both freeway and ramp flows we re counted (Tian et al., 2005). Ringert and Urba (1992) developed am empirical model for estimating the maximum sustainable flow at freeway bottlenecks in Texas, based on the analysis of data collected at several sites. Several results had been obtained. Firstly, f reeway bottlenecks we re the best location for measurement of capacity, as a result of their ability to determine the transition to queue discharge flow. Secondly, turbulence caused by imbalance of traffic (e.g., merging and weaving activit ies ) m ight prematurely transitions the flow from free flow into queue discharge flow. Thirdly, q ueue discharge flow wa s the best estimate of maximum sustainable flow as it had significantly lower variability than free flow rate, and thus wa s recommended as the capacity. And finally, much lower flow rates might occur if the study site wa s affected by downstream congestion. Based on the analysis, a speedflow model was developed and the maximum sustainable flow rate was determined to be 2,200 pcphpl. However, the

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31 result s were based on several as sumptions such as no downstream congestion and that traffic conditions remaining uncongested. With regard to the method of capacity measurement, Hyde and Wright (1986) proposed to estimate capacity by simply selecting the maximum flow rate measured over the observation period or applying expected extreme value method. However, the capacity estimated by this method highly depends on the duration of the average interval. Van Arem and Van der Vlist (1993) proposed to estimate the current capacity by updating the fundamental diagram, which wa s determined under predefined conditions. By calibration, this method can reflect the variance in capacity under different traffic composition s and weather conditions. But this method wa s aimed at estimating capacity while the traffic wa s free flowing, and thus can not estimate the real time capacity during congested conditions. Minderhoud et al. (1997) summarized many methods to estimate capacity (direct empirical and indirect empirical), and found the product limit method, empirical description method and fundamental diagram method to be the ones with highest validity. Further, they discussed the appl i cation of product limit method, in which different traffic states needed to be observed and the bottleneck location should be chosen, in estimating capacity and its distribution based on both flow and speed data. From this viewpoint, this method can provide a good estimation of the capacity because it utilizes the traffic state information and gives a distribution of capacity instead of a single value. The above methods can estimate theoretical capacity, but are not adequate for real time applications such as ramp control, thus real time capacity estimation method

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32 is required. Liu et al. (2008) presented a real time freeway estimation method in freeway ramp control. When the freeway section wa s uncongested with occupancy at the present less than the critical occupancy (averaged around 15.5), 95% percentile of theoretical capacity, which was the maximum flow measured from the flow occupancy diagram, was defined as the capacity. When congestion begins with occupancy exceeding the critical occupancy, operational capacity, which was the actual maximum flow rate and obtained through moving average method based on real time measurements was defined as the capacity. They tested the methodology on the Stratified Zone Metering (SZM) strategy through microsimulator and found that the control strategy improved by decreasing delay and increasing speed. A number of investigations had proven the existence of different capacities under uncongested and congested traffic conditions (i.e. the two capacity hypothesis). The i mplication of two capacities affects the definition and value of capacity. Banks (1990) supported the hypothesis that maximum flow rates decrease d when queues form, and analyzed the capacity drop phenomenon for different NorthAmerican freeways. Capacity drop values of between 3 and 6% were measured. Hall and Agyemang Duah (1991) investigated the issues of whether there wa s maximum flow reduction when a queue forms and where capacity c ould be properly measured. They concluded from data analysis that there was about a 5 to 6 percent reduction of maximum flows at bottlenecks after the onset of congestion, and indicated that capacity can only be measured in a bottleneck but not in a queue. Ponzlet (1996) analyzed traffic flow on German freeways to test whether th e capacity drop phenomenon existed, and a 6% drop of flow rates for 5 minute was determined. Brilon and Zurlinden (2003) analyzed

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33 the capacity drop by comparing the stochastic capacity to flow rates during congested flow and computed an average of 24% capacity drop, which wa s very high compared to other researchers results. Regler (2004) analyzed the capacity drop value using a distribution of breakdown flows and queue discharge flow s, and found an average drop of 250 veh/h i n 5minute flow rates Later, Zhang and Levinson (2004) examined the twocapacity hypothesis about flow drops after breakdown with a dataset of twenty seven bottlenecks. The results showed that the percentage flow drops at various bottlenecks follow a norm al distribution with mean 5.5% and standard deviation 2.3%. Brilon et al. (2005) reported that the capacity drop wa s stochastic, and capacity wa s Weibulldistributed with a nearly constant shape parameter. They further extended this stochastic concept into reliabilities of freeway networks by stating that a freeway may operate at the highest expected efficiency if it wa s only loaded to 90% of the conventionally estimated capacity. Summary In summary, several research studies the definition of freeway capac ity and its distribution. The HCM is the first and most often used document to quantify the concept of capacity T he definition of capacity in this manual varies overtime due to the improvement of facilities as well as the realization of the variance of capacity under different conditions. With respect to the inadequacy of the capacity definition in the HCM, many researche r s suggested defin ing capacity under different traffic conditions h owever, no consensus have b een achieved. Four different flow parameters (maximum pre breakdown flow, breakdown flow, maximum discharge flow and average discharge

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34 flow) are most often used to define capacity, and microscopic characteristics of traffic and drivers are considered to be the reasons of capacity variance at the s ame site. The methods used in measuring capacity include observing maximum flow rates, updating the fundamental diagram, applying product limit method and using real time two phase capacity estimation method, etc. Freeway bottlenecks are considered to be t he best location for measurement of capacity. However, there are still some problems not resolved by previous research: (1) Some research indicated that microscopic characteristics of traffic and drivers, and average time gaps to be the main reason in capacit y variance. More research which quantitatively analyzes the link between the flow variance and its reasons is necessary. (2) Given the concept of freeway capacity randomness, it is necessary to know more about the form of the capacity distribution function. Most of the research does not examine the form of capacity distribution, and there is no research on the impact of site characteristics on the form. The Process of Breakdown and Breakdown Models As referred ear lier f reeway capacity is also related to flow breakdown, which is t he transition between uncongested and congested flow conditions and some researchers suggested taking into consideration the breakdown probability in defining capacity ( Lorenz and Elefteriadou, 2001) The relationship between the prob ability of breakdown at freeway bottlenecks and flow rate is of interest to both capacity analysis and freeway operation. This section reviews previous research related to the process and probability of breakdown. Banks (1991) conducted a study of four bottlenecks in San Diego and suggested that breakdown was triggered by slow moving vehicles that cause unstable speeds in dense platoons. He also observed that breakdown occurs upstream of the merge for three cases and both upstream and downstream of the merge for one case.

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35 Elefteriadou et al. (1995) examined the breakdown occurrence at two freeway ramp merges, using data collected from four video cameras along the ramp merge area. Investigation of the data revealed that the breakdown occurrence was associated with the presence of vehicle clusters coming from the onramp. The ramp vehicle cluster would force its way into the freeway and result in lower speeds. Based on this mechanism, they proposed a probabilistic model, which wa s a smooth S curve and a fu nction of freeway and ramp flow rates. Kerner and Rehborn (1997) studied data collected from detector sensors in the vicinity of freeway ramp merge sections on German highways. They stated that in the vicinity of bottlenecks, the breakdown occurs due to l ocal speed decrease and density increase that is observed when onramp vehicles squeeze on the highway, or due to unexpected speed decrease and lane changing activity. They stated that the latter can result in breakdown even away from a bottleneck. Persaud et al. (1998, 2001) examined the breakdown process over a large number of rush hours at three freeway bottlenecks using detector data. They observed that breakdown was always associated with a sharp decrease in speed and flow and the formation of vehicle queues upstream of the bottleneck. Chung and Cassidy (2004) reported that, based on a study of data from nine days, the breakdown was triggered by high vehicle density that begins from an individual lane and spreads across the freeway segment as drivers change lanes to avoid decelerating. Several models have been developed to predict the occurrence of breakdown. Elefteriadou et al. (1995) developed a model which assumed that breakdown occurs if at least one vehicle on the freeway is forced to reduce its speed by 16 km/h or more.

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36 The probability of breakdown was computed as a function of the cluster size of onramp vehicles and the freeway flow through three steps: calculating the probability of occurrence of all possible cluster size (3 to 15 vehicles), calc ulating the probability that at least one vehicle is present at the critical area of the freeway (the shoulder lane), and estimating the drivers possible actions that they may take as the cluster of vehicles approaches the freeway from the ramps. The resulting model provided the probability of breakdown as a function of freeway and ramp flow rates, and had a smooth S curve shape. The model is illustrated in Figure 24 Evans et al. (2001) used Markov chains to develop the probability distribution of breakd own at rampfreeway junctions based on zonal merging probabilities with respect to the vehicles traveling on the throughway. Lorenz and Elefteriadou (2001) conducted an extensive analysis of speed and flow data at two freeway sections in Toronto, Canada. They observed that the breakdown occurred at various levels of demand and the probability of breakdown increased with increasing flow rate, as shown in Figure 25 Brilon et al. (2005) investigated the relationship between the probability of breakdown and flow using the Product Limit Method ( PLM ) and developed models that predict the probability of breakdown as a function of flow Elefteriadou et al. (2009) developed breakdown probability models for five freeway sections in North America using the PLM, and incorporated the models in ramp metering algorithms. The probability of breakdown was developed as a function of the ramp demand and the freeway demand (considered indiv idually), or as a function of the sum of the ramp and freeway demands upstream of the critical ramp junction, or as a

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37 function of the occupancy upstream of the critical ramp junction. The authors suggested that the type of breakdown probability model to be developed depends on the application purposes. For example, they recommend building a volumebased breakdown model if the breakdown probability model is to be incorporated within a ramp metering algorithm that uses freeway volume for selecting the metering rates; they recommend building an occupancy based model if the ramp metering algorithm to be applied is based on occupancy. In summary, p revious research has associated breakdown with driver actions (braking, lane changing). Breakdown can be observed thr ough a decrease in speed and flow, an increase in vehicle density, and the formation of vehicle queues upstream of the bottleneck. There have been several models reported that predict the occurrence of breakdown as a function of flow, including most recent ly the PLM These models were developed based on several different parameters, including flow and occupancy. The literature review search did not reveal any applications of the PLM for predicting incident induced breakdowns Freeway Capacity and Operation under Incident Conditions Incidents that block freeway lanes or create other impedances to driving behavior s can create significant negative impact on operational conditions such as increased queues, delays and pollution. Incidents can also reduce freeway capacity by blocking one or more lanes and/or the adjacent shoulder lane. This section reviews literature related to the impact of incidents on freeway capacity and the relationship between incidents and operations and proposes pro blems that deserve further research.

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38 Impact of Incidents on Freeway Capacity When an incident occur s, the capacity at the road section may decrease, as probably some lanes are closed. Even if no lane was closed (incidents occur on shoulder) vehicles from upstream may slow down near the incident location, causing capacity reduction as a result of speed reduction. Estimating the freeway capacity following an incident is important for effective traffic management This sub section reviews the impact of incidents on freeway capacity. The HCM 20 1 0 ( also the HCM 2000) addressed the issue of capacity reduction due to incidents as presented in Table 22 This manual reported that the effect of an incident on capacity depends on the length of blocked road section, the number of lanes, drivers slowing down, and the rubbernecking factor. Goolsby (1971) analyzed 27 incidents that occurred between 1968 and 1969 on a 6.5 mile section of the Gulf Freeway in Houston using 1min ute volume counts. Based on these dat a, Goolsby estimated that an in cident or disabled vehicle blocking one of three lanes will result in an average capacity reduction of 50%, an in cident blocking two lanes of three lanes will reduce capacity by an average of 79%, and an in cident or disabled vehicle blocking the shoulder lane on a threelane segment was found to reduce capacity by an average of 33%. T he results obtained by Goolsby are consistent with that given by the HCM and are still widely used by transportation professionals. Both the HCM and Goolsbys research report incident capacity reduction as a deterministic value. Chin et al. (2002) estimated the number of closed lanes based on the type of crash as well as the number and type of vehicles involved. They assumed that a fatal or injur y crash involving more than one vehicle always result in lane closures. The

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39 probabilities of lane closure and number of lanes closed are illustrated in Tables 2 3 and 2 4 However, the estimated probabilities are used for macroscopic estimation of delay and are not suitable for microscopic analysis such as breakdown phenomenon at a specific freeway site. Smith et al. (2003) measured capacity reduction caused by over 200 in cidents that occurred on urban freeways in the Hampton Roads region of Virginia. The authors defined the minimum 10minute flow rate (by moving average of five successive flows to reduce variation) measured in the bottleneck created by an incident as incident capacity and found that : an in cident blocking one of three freeway lanes resulted in a mean capacity reduction of 63% (significantly larger than the widely accepted value of 50% as proposed by the HCM and Goolsbys research in the 1970s), while an in cident blocking two of three freeway lanes resulted in a mean capacity reduction of 77% (similar to Goolsbys research and smaller than that given by the HCM). They also stated that it wa s more appropriate to model incident capacity reduction as a random variable and not a deterministic value due to the v ariation of traffic flow and suggest ed that the beta distribution provides a good representation of in cident capacity reduction for one or two of three lanes blocked. Chin et al. (2004) estimated capacity loss on freeways and principal arterials that result ed from fatal and nonfatal crashe s, vehicle breakdowns, and adverse weather, etc. They assumed that a fatal or injury crash involving more than one vehicle always results in lane closures (i.e., probability of lane closures = 100 percent for injury crashes). Then t hey estimated the number of lanes closed according to the location of crash and crash severity, and calculated c apacity remaining after incident s based on

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40 the total number of lanes available and the number of lanes affected by the crash, as shown in Table 25 In summ a ry, the authors studied capacity loss caused by incident s based on some assumptions about the number of lanes closed. T he study does not consider geometric conditions in capacity estimation. P otter et al. (2007 ) analyzed the number of lanes affected by different i n cident type s. The relationship between incident types and number of lanes affected is shown in Figure 26 Figure 26 A ) shows the percentage of different incidents types in 2005. It was observed that over half (56%) of the incidents were stalls. The next most common types of incidents were crashes (17%) and debris (13%). Figure 2 6 B ) shows the number of lanes broken down by incidents for the year 2005. It was observed that 62% of incidents did not block any lane. T his observation is likely related to the high occurrence of stalls as show n in Figure 26 A ) : 33% of incidents blocked one lane, and only 5% of incidents blocked two or more lanes. Hadi et al. (2007) examined the simulation modeling of incidents and their impacts on capacity. Three types of simulation models we re investigated: CORSIM, AIMSUN and VISSIM These allow the users to simulate incident blockages either explicitly or by using other events that have similar effects on traffic operation. The results show ed that all the three models need to calibrate parameters for the incident location to produce the capacity reduction similar to that estimated by the HCM 2000 or field studies. Only CORSIM include d incident calibration parameters (rubbernecking factor). AIMSUN and VISSIM d id not have incident calibration parameters but had other modeling capabilities (the speeds of the unblocked lanes at the incident locations) that can be used to calibrate the models to produce the identified reduction in capacity due to incidents.

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41 Knoop et al. (2008) collected data about two incidents by helicopter to analyze the impact of incident s on freeway capacity. The result s show ed that the capacity (outflow) at the opposite direction of the in cident location wa s reduced by half by the rubbernecking effect (drivers slow down to see what is happening). The capacity of the road section in the direction of the in cident wa s reduced by more than half, as not all lanes are in use. While most researchers studied the capacity reduction only in the direction of the incident s, this research show ed that the effects in the opposing direction could be of the same order. However, this effect of in cident s on the opposing direction is to be examined on other freeways. T his paper does not make a comparison of the incident capacity reduction observed to the values in the HCM 2000. Relationship between Incidents and Freeway Operations Freeway operational condition can impact safety. Al Deek et al (1995) investigated the relationship between freeway geometry and the location, type, and t ime period of incidents. They found from statistic al analysis that the upgrade freeway segments had significantly higher incident rates than level or downgrade segments, off ramps had significantly higher incident rate than onramps or no ramps, and peak periods had significantly higher incident rates than off peak periods. Many previous researches suggest ed that there wa s a positive association between speed and the risk of crash involvement For example, Solomon ( 1964) studied the relationship between cr ash and speed. They found that crash rates took a U shaped form against the difference in speed and average speed. Crash rate was maximum for vehicles with speeds of more than 35 mph below the average and minimum for speeds of 5 to 10 mph above the average. Kloeden et al. (1997) concluded that "In a 60 km/h

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42 speed limit area, the risk of involvement in a casualty crash doubles with each 5 km/h increase in traveling speed above 60 km/h" There is also extensive research on the relationship between incident f requency and operation al conditions. Chang et al. (2000) clarified the relationship between volume to capacity ratios (v/c) and accident rates at various freeway facility sections, based on data on Shingal Ansan freeway in Korea from 1992 to 1997. The result s show ed that the relationship between accident rates and v/c ratios represented a U shaped pattern for all sections (basic freeway, tunnel, and toll gate sections), as illustrated in Figure 27 They further observed that the accident rate of the toll g ate section wa s generally higher than that of other sections and that there wa s no significant difference in accident rates between the basic freeway and tunnel sections when the v/c is between 0.5 and 0.8. Moreover, the basic freeway, tunnel, and toll gate sections had the minimum accident rates when the v/c rations are 0.78, 0.75, and 0.57, respectively. Garber and Wu (2001) studied the relationship between the crash probability and traffic as well as geometric characteristics based on a selected section of Interstate 64 within Norfolk, Virginia Beach, and Chesapeake in Virginia. The study found that traffic volume, occupancy, standard deviation of speed, and exposure ha d significant positive relationships with the number of crashes, while speed had signi ficant negative relationship with the mean of number of crashes. They also found that the stochastic regression modeling methods c ould be used to describe the probabilities of crash events. Moreover, the authors stressed the use of corresponding traffic data (those occurring at the time of the crashes), as it reflected the true influences of independent

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43 variables on the occurrence of crashes. These findings may help to determine the criteria in incident detection. Golob et al. (2002) developed a tool, call ed FITS (Flow Impacts on Traffic Safety), to evaluate the effect of changes in traffic flow on traffic safety. They classified traffic flow into several conditions, and got the probabilities of different kinds of crash es under different conditions. Continuing their study, Golob et al. (2003) used the tool FITS to forecast the types of crashes that are most likely to occur for the flow conditions being monitored. In applying the tool, they found that crash rate s and types we re related to traffic flow patterns: the highest crash rate happened under heavily congested flow (5.99), then variablevolume congested flow (3.21), and then variablespeed congested flow (2.97). The lowest crash rate happened when flow wa s approaching capacity (0.55). They also st udied the relationship between crash types and mean flow as well as median speed. For example, at flow s higher than mean flow and speed higher than median speed conditions, 78.8% of the crash es happened might be t wo & multi vehicle rear end & lanechange crashes 57.8% of the crashes happened might be t wo vehicle lanechange & rear end crashes The proposed tool developed detail ed relationships among crash rates, crash type s and traffic flow patterns, and can aid in identification treatments that aimed at e nhancing safety. However, future research is needed to compare the present method with other approaches that have been recently developed. Another limitation is that the FITS tool applies only to urban freeways with at least three lanes in each direction G olob and Recker (2003) used linear and nonlinear multivariate statistical analyses to determine how the incident types were related to traffic flow, weather and

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44 ambient lighting conditions based on data from heavily used freeways in Southern California. R esults show ed that the types of collision s were strongly related to median traffic speed and to temporal variations in speed in the left and interior lanes. Controlling for weather and lighting conditions, there wa s evidence that inc ident severity wa s infl uenced more by volume than by speed. Incidents also have impacts on freeway operations. Menendez and Daganzo (2004) used the kinematic wave theory and some dimensional analysis to evaluate how the location and duration of an incident influence delays near a recurrent bottleneck. The incidents are classified according to the delay they incurred to the system. The delay wa s modeled by the intrinsic characteristics of an incident such as capacity at the incident sites, length of rubbernecking zone created by t he incident and free flow speed at the incident site, together with the incident location and duration. However, how to get the capacity at incident site and the length of rubbernecking zone were not illustrated. R esearch on the relationship between conge stion and safety is rich (Jernigan, 1998): Tedesco et al. (1993) noted that reducing congestion can lead to a reduction in secondary crashes. In the event of a crash, the risk of a secondary crash wa s increased by more than 600%. Persaud et al. (1998) stat ed that preserving uncongested operations on freeway result ed in both improved safety and travel time benefits to the trave lers On the other hand, when breakdown occur red and flow transit ed to congested operation, travel times increased as queues form, and in cidents we re more frequent. At two freeway corridors, one in Los Angeles and the other in the Bay Area, incident related delay wa s found to be 13% to 30% of the total congestion delay experienced during peak periods (Prevedouros et al., 2008).

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45 Summary In cident s may lead to capacity reduction, as they usually block lanes and affect other drivers. There is one paper defining the minimum 10minute flow rate (by moving average of five successive flows to reduce variation) measured in the bottleneck created by an accident as incident capacity. Previous research estimated capacity remaining after an incident based on the number of lanes closed by the incident, and report ed incident capacity reduction as a deterministic value. T here is also s uggestion to model incident capacity reduction as a random variable and suggests the beta distribution for one or two of three lanes blocked. The capacity remaining after incidents under various conditions is summarized in Table 26 There has also been r esearch predicting the probability of lane closure and number of lanes closed from type of crashes and number of vehicles involved. The results might be used in this dissertation for sites without information of the number of lanes closed or affected. On the one hand, freeway operations have impact on incidents. On the other hand, incidents also have impact on freeway operations. Incident rate s and types are related to operational conditions such as volume, v/c ratio, speed variation and congestion condition C ongestion can be modeled by the characteristics of incidents. M ost of the studies analyze the whole free way instead of different road sections (e.g., basic section, weaving section on freeway). Limited research studied the effect of incident s on traffi c flow under congested conditions, for instance, the impact of incident s on flow breakdown. Future research on the impact of incidents on traffic flow at freeway bottlenecks under congested condition s is necessary

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46 F urther research is ne cessary in the following areas: (1) Incidents on freeways occur often and they have substantive impact on freeway capacity. However, there is limited previous research on defining freeway capacity under incident conditions. Thus a definition of freeway capacity, which considers the traffic f low patterns, geometric characteristics and incident conditions, is to be proposed. (2) Apart from the number of lanes affected by incidents, it is necessary to estimate capacity remaining after an incident based on other factors, such as geometric conditions the incident duration and type, etc, as there is no clear relationship between them. (3) It is desirable to model capacity remaining after an incident as a random variable rather than a deterministic value because of the variations associated with the incid ent such as traffic control, local conditions and driver behaviors. (4) For sites without information of the number of lanes closed/affected in the dissertation, investigate the potential of predicting the number of lanes closed from incident type and number of vehicles involved. (5) Investigate the relationship between incident frequency and traffic operations at freeway bottlenecks. For example, the frequency of incidents at bottleneck and nonbottleneck locations. Identification and Verification of Incident s T he identification and verification of i ncident s are important in traffic/incident management practice. This section reviews literature related to the detection prediction, and verification of incidents. In cident D etect ion Incident detection is the proces s of determining the presence and location of an incident. The idea has been around since the mid1960s and early 1970s as part of standard traffic/incident management practice. Incident detection algorithms are classified into different types, including comparative, statistical, time series, theoretical models, and a rtificial intelligent algorithms etc (Mahmassani et al., 1999, Ozbay and Kachroo, 1999).

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47 Comparative or pattern recognitionbased algorithm T hese we re first developed by traffic engineers and are by far the more common types of algorithms. Their basic principle is that an incident will create increased occupancy upstream and decreased occupancy downstream of the incident. California algorithms are the best known comparative algorithms. The basic California algorithm was originally developed in the late 1960s ( Payne et al., 1976). It detected incidents by comparing the measured occupancy from two adjacent detectors The general logic of this algorithm is depicted in Figure 2 8 In Figure 2 8 T1, T2 and T3 are site specific occupancy values that need to be calibrated from empirical data. Payne and Tignor (1978) modified the California algorithm and published 10 new versions, among which No. 7 and No. 8 were the two that performed best Mahmas sani et al. (1999) reviewed the literature and concluded that the comparative algorithms work best under moderateto heavy traffic conditions but cannot handle fluctuating traffic demands efficiently as they rely on static thresholds Th ese algorithms ar e most widely implemented and have been installed in California, Chicago, and Tex a s (Martin et al., 2001). Statistic algorithms T hese algorithms model the stochastic traffic flow patterns obtained from loop detector data. Such algorithm s include the S tandard N ormal D eviation algorithm that is based on mean and standard deviation of occupancy (Dudek et al., 1974), and the Bayesian algorithm that is based on the relative difference in occupancy ( Levin and Krause, 1978). T ime series algorithms This kind of algorithm considers the recent history of a traffic variable and employs statistical forecasting of traffic behavior to provide short -

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48 term traffic forecasts (Mahmassani et al., 1999) Such algorithms include the High Occupancy ( HIOCC) algorithm that is based on occupancy ( Collins et al. 1979) the Autoregressive Integrated Moving Average (ARIMA) algorithm that uses occupancy (can also use volume or speed) to detect incidents (Ahmed and Cook, 1982), and the D ouble E xponential algorithm that uses onemin ute average volume, occupancy and speed ( Cook and Clevelend 1974) The D ouble E xponential algorithm has been implemented in Toronto (Martin et al., 2001). Another is the Low pass Filter algorithm developed by Stephanedes and Chassiakos (1993) which is based on occupancy Traffic (modeling) and theoretical algorithms T hese employ the basic theories of traffic flow characteristics. The most notable one among these is the McMaster algorithm (Persaud and Hall, 1989). It was based on the catastrophe theor y that sudden changes could occur in one variable of interest (in this case the speed) while other related variables (in this case the flow and occupancy) exhibit smooth and continuous change. Generally, this algorithm classifies traffic operation on the f reeway into four states using volume and occupancy. Once congested operation is detected at any detector, operations at the downstream detectors are evaluated to identify whether the congestion was caused by an incident or not. The algorithm requires calib ration of the boundaries separating different traffic conditions at each detector (Mahmassani et al., 1999, Parkany and Xie, 2005). It has been implemented in Minnesota (Martin et al., 2001). Other algorithms Artificial intelligent based algorithms use input data of traffic flow variables to get associated output result s This kind of algorithm includes Neural Networks ( Dia and Rose, 1997) and Fuzzy algorithm s (C hang et al., 1994). Wavelet

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49 techniques, which are usually used in detecting changes in signals in electrical engineering have also been used to detect incidents ( Teng and Qi 2003, Jeong et al. 2009) Mahmassani et al. (1999) suggested combining existing algorithms to achieve the advantages of different algorithms in incident detection. This process is termed Algorithm Fusion. A utomatic incident detection algorithms are usually evaluated using three measures : detection rates (DR), false alarm rates (FAR) and mean time to detect (MTTD). DR is the proportion of detected incidents to the total number of actual incidents during a given time period. False alarm rate (FAR) has different definitions for different applications. It has mostly been defined as the ratio of the number of false alarms to the total number of algorithm applications ( off line FAR ). It has also been defined as the fraction of the number of false alarms to the total number of declared incident alarms, including all correct and false alarms ( o n line FAR) Finally it has also been defined as the number of false alarms per day or per hour. M TTD is defined as the average time spent from the moment an incident occurs until the time that the algorithm declares this incident, averaged for all incidents detected over a period of time and measured in minutes ( Balke, 1993; Parkany and Xie, 200 5) In previous research, t he algorithms are usually tested with simulation data or/and field data. The best perform ing commonly used algorithms are summarized in Table 2 7 This t able uses the definition of off line FAR. Howe ver, it i s not clear based on the literature reviewed which of the algorithms are tested with simulation data or field data. As shown in Table 2 7 almost all the algorithms have the limitation of false incident prediction. This occurs because t here wa s a large overlapping area in which

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50 traffic stream variable measures are the same during both non incident and incident operations ( Cook and Cleveland, 197 4) Guin et al. (2004) conducted a survey to personnel in Transportation Management Centers all over the United States and the Ontario Ministry of Transportation at Ontario, Canada, to evaluate the status of existing implementation of incident detection algorithm s. There were 32 centers responding to the survey, with the viewpoint that the unacceptably hi gh false alarms rate is the major deterrent of incident detection algorithms, and, on an average, a maximum of three false alarms per hour and an average of ten false alarms per day are considered acceptable. Brydia et al. (2005) also conducted an automati c incident detection survey. With respect to the acceptable number of false alarms that operators are willing to accept, per day, per station, the predominant (60%) answer was two to five. In conclusion, there is a significant amount of research on incident detection. The California algorithms and McMaster algorithms a re the mos t widely known and relatively simple compared to more recently developed algorithms These two are often used as a standard to evaluate newer algorithms The literature review search did not reveal any applications of the PLM for the detection of incidents It is also concluded from the literature that occupancy is most often used in incident detection. Other traffic parameters used for incident detection include volume, speed, and standard deviation of occu p ancy In cident Prediction Real time incident prediction is the process of using current operational data analysis to predict the probability of an incident during the following time period. Several methods have been developed and used to predict incident occurrence.

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51 Liu (1997) predicted the likelihoods of two types of incidents for a particular period on a specific section on the freeway using a binary logit model. Parameters found to be significant in predicting overheating vehicle incidents included peak factor, merge, temperature, rain, and speed variance, the value is 0.215. Parameters found to be significant in predicting vehicle crash incidents included merge operations visibility, and rain, the va lue is 0.14. Traffic variables such as flow are not significant in crash incident prediction. However, the data are hourly recorded and thus lack precision. As pointed out by the author, the hourly data levels out the large changes in other parameters such as average speed, flow and speed variance at the beginning of incident. The developed incident likelihood prediction models are evaluated by both mathematical formulation and simulation, and found that the reduction in incident waiting time (incident detection plus response time) is significant when the models are used. The model results are not compared with other researches. Oh et al. (2001) used a nonparametric Bayesian modeling approach to predict the real time incident likelihood based on real time traffic data and incident data for the I 880 freeway in Hayward, California. The authors clas sified traffic conditions into two patterns: disruptive (a 5minute period right before an incident) and normal (a 5minute period 30 minutes before an incident occurrence). They used the 5minute standard deviation of speed (selected from six candidate pr ecursors: the mean and standard deviation of three traffic parameters flow, occupancy, and speed) to identify incidents. The model is applied to real time detector data, and the results show that there are some false predicted incidents. The model results are not compared to other researches. However, insufficient data led to some key assumptions and thus limited

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52 the scope of the study. Moreover, it used only the standard deviation of speed as the incident indicator, which cannot completely define traffic o peration. Lee et al. (2003) developed a log linear model using categorical variables for incident prediction. They investigated three crash precursors in the model: the average variation of speed on each lane (measured by the coefficient of variation of s peed, CVS), traffic density (D), and average speed difference between upstream and downstream ends of the road section (Q). Each parameter was classified into several categories. They also investigated exposure (the product of daily traffic volume and the length of each road section), and two control factors: road geometry and time of day. They found the average variation of speed on each lane (CVS) and traffic densities to be significant incident predictors, and that CVS has a relatively longer term effect on crash potential than either D or Q. Also, higher level crash precursors contribute to higher crash potential than lower level crash precursors. The developed model was calibrated for historical crash data using the maximum likelihood estimation method, but not used to predict crash potential in real time using the current traffic flow data. Another problem is that, instead of predicting the potential of an incident occurring during the following time intervals, the model predicted the number of incident s per vehicle kilometers of travel Balke et al. (2005) used a binary l ogit model to predict incident s using loop and weather data. They tested average volume, average occupancy average speed, and CVS, using different detection time and moving average window size. The estimation results indicated that occupancy and average variation of speed are potential precursors of crashes and the model fitted best when using 15minute detection time

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53 and 5minute moving average. The modeling results are shown in Table 2 8 The model was tested with both incident and nonincident data. An example of a fiveday data set test is shown in Figure 2 9 A collision incident was reported on October 12, 2004, at 1:06 PM. The authors concluded that the model predicts high likelihoods of collision quite accurately. However, how to distinguish incidents from congestion was not investigated. This model might c ause false prediction of incidents during unstable traffic flow, which may have high average CVS value. The model results are not compared with other researches. Pande et al. (2005) used logistical regression model to measure the hazard ratio at different locations around the incident and at different time slices 30minutes prior the incident, based on 2046 crashes collected from 4 years on Interstate 4 in Orlando, F l orida. The log CVS, standard deviation of volume and average occupancy were found to be the most significant variables affecting the crash odds. The parameters calculated from 5 minute level were more significantly correlated with crash than that calculated from 3 minute level. It was observed from the spatiotemporal analysis that the crash odd increased as the time and location of the crash were approached. Thus the authors recommended to implementing measures to reduce the speed variance, once a potential crash location was identified in real time. Abdel Aty et al. (2005) extended this methodol ogy to predict freeway crashes under low speed regime (near 25 mph) and high speed regime (near 55 mph). Different models were developed for the two regimes using logistic regression and it was found that different parameters were kept in the final models.

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54 Kuchangi (2006) used a categorical log linear model to predict the incident probability. The parameters used were exposure in vehiclemiles of travel, CVS, occupancy, geometric indicator (onramp, off ramp), peak hour factors. Each parameter had several c ategories. The results showed that t he rate of crash occurrence increased with CVS and occupancy. Occupancy was regarded as a stronger precursor to predict incidents than CVS as it ha d larg er range between maximum and minimum estimates Crash rate was low er during nonpeak hours than during peak hours and was lower at straight sections or sections without onramps and off ramps than at curved sections or sections near to ramps. Overall, roadway type indicator and peak hour indicator we re less sensitive wh en compared to CVS and occupancy. The parameter exposure was found to be statistically insignificant. However, the developed model predicted the number of crashes at different categories of the parameters but not the real time crash likelihood, and the m odel was not validated. Pande et al. (2011) examined the relationship between crash risk and real time traffic variables from a freeway corridor based on loop data collected from I 4 eastbound in Orlando, FL They considered nine parameters (average, stan dard deviation and logarithm of coefficient of variation for speed, volume and occupancy) and developed a variable selection procedure based on random forests Average occupancy of upstream station average speed and coefficient of variation of volume for downstream stations were found to have significant effect on crash risk. The developed model is also applied to three other freeway corridors (I 4 westbound, and I 95 north and southbound). The results showed that the model developed for I 4 eastbound cor ridor works good for the I 4 westbound corridor however, the performance is not as good for I 95. They then

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55 suggested that the same model for crash risk identification may only work for corridors with very similar traffic patterns. There had also been research regarding incident type prediction. Pande and Abdel Aty (2006) used neural networks to develop models for predicting the rear end crash risk. They found that, in congested conditions, the average occupancy and average variation of speed at the location (loop detector station) of interest were the most important variables affecting the rear end crash risk. While in no n congested conditions, the speed difference wa s very important, as the crash risk was increased when faster moving vehicles approaching slower moving vehicles. Thus average speeds at the location of interest and both upstream and downstream of this location we re required. They also used a single neural network model to predict lanechange crash es, and found that the main factors affecting the lanechange crash risk we re the average speeds upstream and downstream of the station of interest as well as the difference in the lane occupancies across each individual lane on the freeway. The higher the absolute difference in the lane occupancy across adjacent lanes on freeway, the higher the chance of having a lanechange related crash. However, there was one research by Luo and Garber (2006) reporting that incidents cannot be predicted. They used three pattern recognition methods : the K means clustering Method, the NaveBayes Method and the Discriminate Analysis to differentiate crash leading pattern from normal noncrash pattern. They extracted 391 crashes as well as the same number of noncrash cases from detector data, and used 45 minutes of detector data (in 1 min interval) preceding each crash in identifying the potential crashleading traffic pattern. Six variables were considered: the mean and

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56 variance (5 min) of occupancy, volume and speed. They found that, when considering only one variable, the distributions of each variable for both crash and noncrash cases 15 minutes prior to a crash are similar. That is, they w ere unable to identify the potential crash leading pattern from the normal pattern based on one single variable. They also considered two variables and all the six variables with the combination of different time periods, however, none of the three methods could distinguish the crashleading pattern from the normal noncrash pattern, and t he overall classi fication error rate remained above 50 %. They further explored the reason and suggested two possibilities : (1) limited s ample size of the normal noncrash cases ; (2) t he spatial difference of the traffic flow as they found that 68% of the crashes didn t sh owing any significant change in the traffic flow patterns after the crash occurred. In summary, research has investigated the prediction of i ncidents based on several parameters of operational conditions. In particular, one research investigated the predic tion of one specific type of i ncidents crash. The most often cited as significant factors in predicting incidents are occupancy, CVS and standard deviation of speed. Other significant factors include standard deviation of volume, the speed difference between upstream and downstream, average speed coefficient of variation of volume standard deviations of time headway Methods such as Bayesian analysis, log linear models, binary logit models and neural networks have been used for predicting incidents. M ost of the literature do not divide traffic states, while two researches develops different models for non congested and congested conditions. The literature review search did not reveal any applications of the PLM for predicting the

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57 probability of incidents There was also one research reporting that incidents cannot be predicted. In cident Verification Incident verification is one of the first steps in traffic incident management. It is the determination of the precise location and nature of an incident ( Carson, 2009). It includes the verification of the time, location, and effect of an incident. (1) Verification of I ncident T ime Lee et al. (2003) developed a log linear model using categorical variables for incident prediction, based on data of a 13month period collected at 38 loop detector stations along the Gardiner Expressway in Toronto They observed from data analysis that there was speed drop occurr ing when a queue formed after the crash occurrence and the backwardmoving shock wave passed over the nearest upstream detector station. They then reported to consider the time when the speed abruptly dropped at the detector station immediately upstream of the crash site as the estimate of the actual time of crashes. The determination of incident tine was usually based on observations of occupancy vs. time series plots of the incidents, as shown by the research of Shaik (2003) and Masinick and Teng (2004). An example wa s shown in F igure 2 10. Figure 2 10 show ed whether a significant increase or decrease in occupancy was present in the travel direction. The beginning and ending points of the increase were visually determined for each incident, with the cutoffs representing the effective duration of the incident. However, the determination of the critical occu pancy rate wa s not illustrated. T here was no specific method to determine the value of occupancy increase

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58 during an incident occurrence. Another difficulty was that it is hard to tell whether the increase in occupancy was caused by incident or recurrent co ngestion. (2) Verification of I ncident L ocation This determination wa s based on the observation of sudden significant change in occupancy between upstream and downstream stations. Specifically, it wa s perceived that the station immediately upstream of ea ch incident location would have the earliest and largest occupancy change, while occupancy change at subsequent upstream stations would start at a later time due to the backward moving shockwave ( Masinick and Teng, 2004) An example wa s shown in Figure 2 1 1 The increase in occupancy at Station A was earlier than that at Station B and Station C, indicating that Station A wa s the immediate upstream station of the incident. However, multiple incident periods c ould give misleading results and thus need further treatment (Masinick and Teng, 2004). It is better to check the change in occupancy downstream, the flow and speed patterns as well. (3) Verification of I ncident I mpact After the verification of incident time and location, it is also necessary to determine whether an incident had significant impacts on capacity and traffic flow patterns. There was no previous literature regarding verifying the impact of incidents on freeway flow. One research related to this ve rification was conducted by Masinick and Teng in 2004. He used a binary logit model to determine the rubbernecking likelihood of an incident and the significant variables that might cause rubbernecking. The result s show ed that four variables significantly influence whether an in cident impact the traffic

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59 in the opposite direction, they we re peak hour weather, presence of barriers, and weekend. As reported by Carson (2009), the effectiveness of incident verification by loop detector data was ver y low to moderate. Thus several other methods of incident verif ication were also used in traffic incident management For example, using onsite response personnel and remotely using closedcircuit television (CCTV), which have reported effectiveness of moderate to ver y high. Summary In conclusion, there wa s a significant amount of research on incident detection. Most of the algorithms are spatial measurement based algorithms Incidents are mainly detected based on occupancy. The California algorithms and McMaster algorithms a re the most widely known and relatively simple compared to the later developed algorithms and are often used as a standard to evaluate the other algorithms Most incident detection algorithms perform best in low to medium traffic volumes, while some work better in high volumes The same algorithm might work di fferently at different geometric locations. One of the possibly serious problems in automatic incident detection is the "false alarm", in which an incident is signaled when one has not taken place. The literature review search did not reveal any applicatio ns of the PLM for the detection of incidents The method or/and parameters often used in incident detection are summarized in Table 29 Previous research on incident prediction is not so rich as on incident detection. Incidents are predicted from one or s everal parameters of operational conditions. There has also been research predicting the probability of one specific type of incident. The

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60 most often used criteria in predicting incidents are occupancy and the variance of speed, as summarized in Table 2 1 0 The time and location of incidents are mainly verified by occupancy. The time of incident occurrence can also be determined as the time when speed drops at the detector location immediately upstream of the incident location. S everal other methods such as onsite response personnel and remotely using closedcircuit television (CCTV) are also used in incident verification. No previous research verifies the impact of incidents on operations to separate minor incidents from major incidents. Future research should examine the following areas: (1) Investigate whether incidents could be detected using other methods such as the PLM It is recommended to divide traffic operation into different states, e.g., noncongested and congested conditions, and develop different algorithms for different conditions separately. Some other parameter s such as the difference between speed limit and speed m ight be considered. Nonlinear form of the parameters such as quadratic form might also be considered in detecting incidents. (2) Insufficient data is also a weakness of previous research. Sufficient data from several freeways should be used to take into cons ideration the effect of geometric characteristics. (3) Develop criteria of verifying the impact of incidents on operations. This method might help to avoid unnecessary analysis of minor incidents. Ramp Management Strategies Responsive to Incidents A large var iety of incident management strategies had been developed to mitigate the impact of incidents on freeway operations For instance, information dissemination with variable message signs (VMSs) or highway advisory radio, measures of reducing the clearance ti me of incidents, and operational strategies such as temporary opening of high occupancy vehicle lanes to general traffic (Boyles et al., 2008) This section reviews literature related to ramp management strategies responsive to incidents, including ramp cl osure and ramp metering.

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61 Ramp Closure One commonly used strategy t o improve traffic flow during incident conditions was to clos e onramps which dates back to the early 1960s (Boyles et al., 2008). Miesse (1967) conducted a micro simulation analysis to st udy the improvement attained from ramp closure. Michigan Department of Transportation conducted experiments in early 1960s on peak hour ramp closure in Detroit, and found substantial increases in freeway throughput (up to 13.7%) and freeway speed (10 mph) without creating excessive problems on the arterials (Gervais and Roth, 1966). Ritchie and Prosser (1990) developed a Freeway Real Time Expert System Demonstration (FRED) for managing nonrecurring congestion on urban freeways in Southern California. A real time ramp metering, which can operate independently and only be interceded when the local capacity has been drastically reduced by an incident, wa s applied respons ive to an incident in the FRED system. When an incident occur red ramps upstream m ight be recommended for closure to reduce the demand at the incident site, and if the severity of the incident wa s above a specified threshold, all ramps within a certain distance upstream of the incident we re recommended for closure. Boyles et al. (2008) developed a twophase procedure intended to guide the process of closing ramps in response to incidents. The first phase identifie d the best combination of onramp s to be closed in response to an incident on a freeway section, using the total system travel time as measure of effectiveness. The second phase attempt ed to find the best length of time to close the ramps, using microsimulation to study the vicinity of incident s in greater detail. The results showed that traffic operation was improved (traffic density i s decreased) by closing the ramps during the incident.

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62 However, their procedure wa s based on many assumptions, e.g., the incident duration wa s known. Ramp Metering Another ramp management strategy to respond to incidents is ramp metering. Chang et al. (1994) proposed an integrated real time ramp metering algorithm, which could capture the dynamic traffic states with a twosegment linear flow density model and thus provide timevarying metering rates, for nonrecurrent freeway congestion. The eff ect of the incidents was considered by multiplying the mean flow rate with the incident factor that represents capacity reduction as a result of incidents. Metering rate was then obtained through optimization. The evaluation results showed that the propose d algorithm can increase freeway throughput, and the effectiveness increased with the severity of incidents and level of congestion. Bogenberger et al. (2001) developed new adaptive fuzzy algorithms named Adaptive and Coordinated Control of Entrance Ramps with Fuzzy Logic ( ACCEZZ ) and evaluated their effectiveness under incident scenarios for a particular 26 km freeway segment located on the northbound direction of Autobahn No. 9 (A9) in Munich, Germany by the microscopic simulator AIMSUN2 T h e severity ( indicated by the number of lanes blocked) and the duration of the incident s w ere assumed to be detected immediately by an incident detection algorithm contained in the traffic management system and exactly estimated The ACCEZZ models consider e d the effect of an incident through a suitable modification of the fundamental diagrams. These modifications included the implementation of special incident rates, incident capacities or desired incident occupancies etc. Then the ramp metering rates of th e upstream onramps were immediately adjusted. The evaluation results showed that the ramp

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63 metering substantially improved the freeway system performance by reducing the total time spent in system The effects of existing ramp metering algorithms responsiv e to incidents were also studied. Chu et al. (2004) evaluated the effectiveness of several ramp metering algorithms under the non recurrent incident scenario. They concluded that adaptive ramp metering algorithms: ALINEA and BOTTLENECK, cannot improve syst em travel time and freeway travel speed effectively under incident scenario, as the effectiveness of ramp metering was marginal during severe congestion conditions. T he coordinated algorithm BOTTLENECK perform ed slightly better than the adaptive algorithms because the coordinated algorithm can respond to both local congestion and congestion appealed in a coordinated area. They further stated that traveler information systems we re important for reducing traffic congestion caused by incidents. Michalopoulos et al. (2005) studied the effect of incidents on the performance of Stratified Zone Metering (SZM) Strategy by setting artificial incidents in the microscopic simulator AIMSUN. Each incident was assumed to cause blockage of lane(s) over a certain period of time and occur on the rightmost lane at 17:00:00. The incident severity was measured by duration of 10 minutes to 60 minutes with an increment interval of 10 minutes. The simulation results showed that the mainline, ramp and system total travel time increase d steadily as incident duration increases and that an incident downstream of a bottleneck wa s more detrimental to control performance than an upstream incident. However, the authors didn t provide adjustments of the SZM strategy in response to inc idents.

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64 Ramp metering can also impact freeway operation safety. Lee et al. (2006 ) used a log linear crash prediction model to investigate the effect of the local traffic responsive ramp metering strateg ies on freeway safety. The results showed that ramp m etering reduced crash potential by 5% 37% compared to the noncontrol case. The results provided some insight into how a local ramp metering strategy can be modified to improve safety (by reducing total crash potential) on longer stretch of freeways over a wide range of traffic conditions. However, the researchers only analyzed the effect of ramp metering control ALINEA on freeway safety, the effect of other algorithms on safety wa s not examined; Moreover, they used only one crash potential (speed differenc e) in the crash prediction model, and cannot reflect the relationship between crash and traffic flow accurately Another limitation was that the microscopic simulation models used (PARAMICS) had not been sufficiently calibrated and the car following behavi or wa s not realistic. Summary Ramp clos ure is a ramp management strategy that is mainly used in response to the occurrence of incidents. Another approach is ramp metering. Generally, this method adjusts capacity under incident conditions by multiplying the mean flow rate with the incident factor that represents capacity reduction as a result of incidents (i.e., use a two segment linear flow density model ), or through a suitable modification of the fundamental diagrams The corresponding metering rate is then adjusted or calculated from optimization. The evaluation results show that the adjustment can improve the system performance. Some existing ramp metering algorithms such as BOTTLENECK and ALINEA also show the ability or potential to improve system perfo rmance under

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65 incident conditions. Moreover, ramp metering can also impact freeway operation safety by reducing crash potential. Areas deserve further research include: (1) To incorporate the capacity under incident condition and breakdown probability into the ramp metering algorithm. This application may delay or prevent the occurrence of breakdown and thus increase freeway throughput. (2) Take into consideration the location of incidents in ramp metering. For instance, when incident occurs downstream of the bottleneck, the metering rate upstream should decrease, while when incident occurs upstream of the bottleneck, the metering rate might increase. (3) Evaluate the effectiveness of ramp metering strategy that responsive to incidents using field data collected from several sites. This may help adjust and implement the proposed ramp metering strategy.

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66 Table 2 1 Summar y of t he l iterature on capacity d efinition Authors Definition of capacity Data Persaud and Hurdle (1991) Mean discharge flow 3 days data collected from a three lane freeway Agymang Duah and Hual (1991) 2300 pc/h/ln under stable flow; 2200 pc/h/ln for post breakdown conditions Data of over 52 days during peak period Minderhoud et al. (1997) Non congested flow data were used to estimate the capacity distribution N/A Cassidy and Bertini (1999) Suggested the long run queue discharge flow as the bottleneck capacity 3 days data collected from two freeway bottlenecks in Toronto Lorenz and Elefteriadou (2001) Flow rate corres ponding to the expected probability of breakdown deemed acceptable More than 40 congestion events occurring during about 20 days at two freeway bottlenecks in Toronto Elefteriadou and Lertworawanich (2003) Breakdown flow, maximum prebreakdown flow, maxim um discharge flow More than 40 congestion events occurring during about 20 days at two freeway bottlenecks in Toronto Kerner (2004) Homogeneous segments: free / synchronized flow/wide moving jams Bottlenecks: determined by transition from free flow to synchronized flow, an infinite number of capacities On highway A5North in Germany Brilon (2005) Variable, considered only the volumes that cause breakdown as capacities Data of year 2000 collected from two freeway sections Brilon et al. (2005) The traf fic volume below which traffic still flows and above which the flow breaks down, Weibull distributed Data of year 2000 collected from two freeway sections Banks (2006) Pre queue flow and queue discharge flow 18 extended data collection periods at 15 bottl enecks in North America Yeon et al. (2007) Maximum pre breakdown flow, breakdown flow, maximum queue discharge flow and average queue discharge flow Speed and volume data from May 2004 to August 2004 on US 202 SB near Philadelphia, PA

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67 Table 22 Portion of freeway capacity available under incident conditions (Source: HCM 20 1 0 HCM 2000 ) Number of freeway lanes by direction Shoulder disablement Shoulder accident One lane blocked Two lanes blocked Three lanes blocked 2 0.95 0.81 0.35 0.00 N/A 3 0.99 0.83 0.49 0.17 0.00 4 0.99 0.85 0.58 0.25 0.13 5 0.99 0.87 0.65 0.40 0.20 6 0.99 0.89 0.71 0.50 0.26 7 0.99 0.91 0.75 0.57 0.36 8 0.99 0.93 0.78 0.63 0.41 Table 23 Probability of lane closure due to crashes and breakdowns (Source: Chin et al., 2002) Type of crash Number of vehicles involved Lanes closed No lane closed Fatal crash 1 vehicle 0.892 0.108 More than 1 vehicle 1.000 0.000 Injury crash 1 vehicle 0.892 0.108 More than 1 vehicle 1.000 0.000 Property damage only Less than 3 cars and at most I truck 0.600 0.400 3 or more c ar s and /or 2 or more trucks 1.000 0.000 Breakdowns N/A 0.154 0.846 Table 24 Probability distribution of number of lanes closed (Source: Chin et al., 2002) Number of vehicles involved Type of vehicles involved Lanes closed 1 2 3 4+ 1 Vehicle Any type 0.997 0.001 0.001 0.001 2 Vehicles 2 cars, or 1 car and 1 truck 0.950 0.048 0.001 0.001 2 trucks 0.001 0.997 0.001 0.001 3 Vehicles 3 cars, or 2 cars and I truck 0.500 0.450 0.049 0.001 1 car and 2 trucks or 3 trucks 0.001 0.600 0.300 0.099 More than 3 Vehicles Any type 0.001 0.099 0.800 0.100

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68 Table 25 Capacity remaining after incidents ( nonincident capacity = 1.000) (Source: Chin et al., 2004) Effect of c rash Number of f reeway l anes 1 2 3 4 5+ Vehicle on the shoulder 0.450* 0.750 0.840 0.890 0.930* 1 lane blocked 0.000 0.320 0.530 0.560 0.750 2 lanes blocked N/A 0.000 0.220 0.340 0.500 3 lanes blocked N/A N/A 0.000 0.150* 0.200* 4 lanes blocked N/A N/A N/A 0.000 0.100* (* Assumed) Table 2 6 Percent of freeway capacity available under incident conditions Time Number of lanes Lane closed shoulder 1 lane 2 lanes 3 lanes Goolsby, 1971 3 0.67 0.50 0.21 0.00 HCM 20 1 0 2 0.81 0.35 0.00 N/A 3 0.83 0.49 0.17 0.00 4 0.85 0.58 0.25 0.13 5 0.87 0.65 0.40 0.20 Smith et al., 2003 3 N/A 0.37 0.23 N/A Chin et al., 2004 2 0.75 0.32 0.00 N/A 3 0.84 0.53 0.22 0.00 4 0.89 0.56 0.34 0.15* 5 0.93* 0.75 0.50 0.20* (* Assumed)

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69 Table 2 7. Performance of some common incident detection algorithms (Sources: Subramaniam, 1991; Balke, 1993; Ozbay and Kachroo, 1999; Jeong et al. 2009) Type Algorithm Detection r ate False a larm r ate Mean t ime to d etect (min) Comparative California Basic 82% 1.73% 0.85 California No. 7 67% 0.134% 2.91 California No. 8 68% 0.177% 3.04 Statistical Standard Normal Deviate (SDN) 92% 1.3% 1.1 Bayesian 100% 0% 3.9 Time series Autoregressive Integrated Moving Average (ARIMA) 100% 1.5% 0.4 Smoothing Double Exponential Smoothing 92% 1.87% 0.7 Filtering 95% 1.5% 0.67 Low pass Filter (LPF) 80% 0.3% 4.0 Traffic modeling McMaster 68% 0.0018% 2.2 Artificial intelligent Probabilistic Neural Networks (PNN) 89% 1.2% 0.9 Jeong et al. (2009) Wavelet based 95% 1% 1.34 Table 2 8. Estimated binary logit model for collision incident (Source: Balke et al., 2005) Variables Estimated Coefficient t ratio P value Constant 2.508 9.150 0.0000 Average Occupancy (%) 0.139 4.776 0.0000 Average CVS 14.251 3.703 0.0002 Number of observations 380 Restricted log likelihood 212.58 Log likelihood at convergence 186.68

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70 Table 2 9. Summa ry of research on incident detection Authors Algorithm n ame Criteria u sed Advantage / Disadvantage West (1969) California algorithm 2 Occupancy from two adjacent detectors Advantage: Simple, good performance and low false alarm rate; Disadvantage: cannot distinguish incident congestion and recurrent congestion Payne and Tignor (1978) California algorithm 7,8 Temporal differences in occupancy, downstream occupancy Advantage: Simple, good performance and low false alarm rate; Disadvantage: cannot distinguish incident congestion and recurrent congestion Persaud and Hall (1989) McMaster algorithm The pattern of flow, occupancy data Advantage: effective at distinguishing traffic incidents from recurring traffic congestion ; Disadvantage: requires a shift from uncongested to congested operation Chassiakos and Stephanedes (1993) Filter algorithm Spatial occupancy difference between adj acent stations Advantage: effective at distinguishing traffic incidents from recurring traffic congestion, excellent DR and FAR rates; Disadvantage: long detection time

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71 Table 2 10. Summa ry of research on incident prediction Authors Data / Tool used Incident prediction criteria Liu (1997) Incident data, traffic data, weather data Binary Logit Model Over heating vehicle incident: peak, merge, temperature, rain, speed variance Vehicle crash incident: merge, visibility, rain Oh et al. (2001) Accident data, real time traffic data Bayesian modeling 5 minute standard deviation of speed Lee et al. (2003) Categorical log linear model Lane by lane variation of speeds (CVS), traffic densities Balke et al. (2005) Integrated loop and weather data Binary Logit model Occupancy, average variation of speed Pande et al. (2005) Loop data. Logistic regression 5 min log CVS, standard deviation of flow, average occupancy Abdel Aty et al. (2005) Loop data. Logistic regression Low speed region: log of CVS and aver age occupancy, standard deviation of speed; High speed region: log of average occupancy, standard deviation of speed, average speed Kuchangi (2006) Loop data, incident log. Categorical log linear model CVS, occupancy, peak hour indicator, roadway indicator Pande and Abdel Aty (2006) rear end crashes Congestion condition: traffic data of the studied location Average occupancy, average variation of speed Non congestion condition: traffic data at the studied location and up to 1 mile upstream and downstream Average speeds, average occupancy lanechange crash Average speeds upstream and downstream of the station, difference in the lane occupancies across each individual lane

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72 Figure 2 1 Illustration of three parameters on timeseries plot of flow and speed (Source: Elefteriadou and Lertworawanich, 2003) Figure 2 2 Probability of F S transition and the corresponding capacity (qsum= qin + qon, that is, the mainline flow plus the onramp flow) (Source: Kerner, 2004)

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73 Figure 2 3 Capacity distributions for a 3lane freeway with and without variable speed control (13.5% average truck percentage, 5minute interval) (Source: Brilon et al, 2005) Figure 2 4 Probability of breakdowns in 15 min by Elefteriadou et al., reproduced (Source: Elefteriadou et al, 1995)

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74 Figure 2 5 Probability of breakdown versus observed flow rate Site A (Source: Lorenz and Elefteriadou, 2001) A B Figure 2 6 R elationship between incident types and number of lanes affected A) Incidents by type, B) n umber of lanes affected (N=17,885) (Source: Potter et al, 2007 )

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75 Figure 2 7 Relationship between v/c and accident rate at basic freeway section (Source: Chang et al., 2000) Figure 28 Structure of basic California incident detection algorithm ( Payne et al., 1976)

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76 Figure 2 9 Predicted collision likelihood (Source: Balke et al. 2005 ) Figure 2 10. Example of i ncident o ccupancy (Source: Masinick and Teng, 2004)

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77 Figure 2 11. Incident caused o ccupancy at m ultiple stations (Source: Masinick and Teng, 2004)

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78 CHAPTER 3 D ATA COLLECTION AND METHODOLOGY As mentioned in chapter 1, t he study on the impact s of incident s on freeway capacity and flow breakdown will depend largely on the analysis of data. This chapter illustrates t he requirements of data types and collection sites, and presents the data analysis procedure. Database Overview Data collected from five freeway sections for the NCHRP 3 87 project Proactive Ramp Management u nder the Threat of Freeway Flow Breakdown (Elefteriadou et al., 200 9 ) are used for this dissertation. The data are described in Ta ble 3 1. Type of Data At each site, three main types of data need to be obtained which are traffic data, incident data, and weather data. Traffic data: include flow, occupancy and speed from all available detector stations along the selected sections. T raffic data are mainly collected from l oop detector s and downloaded from corresponding websites Incident data: include the information about the number of incidents, incident type and duration, etc., at the study site. T h ey are collected from traffic data maintenance websites or incident log s developed by the local incident management center. Weather data: include average daily weather index such as the rain fall, snow, visual condition (fog, smoke, etc) at the data collection sites. The weather data are downloaded f ro m the National Oceanic and Atmospheric Administrations (NOAA) National Weather Service website (http://www.weather.gov/). At some data collection sites, the geometric data and ramp management strategy ( i. e., metering strategy and metering r ate) can be collected. To cover the full change of traffic flow patterns and process of breakdown, the data are collected 24 hours daily or

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79 at least from 6 AM to 7 PM. The data should also be available for about one year for the breakdown model development S ite Descriptions According to the objective of the NCHRP 387 project, t he data collection site should be a freeway section that contains bottleneck, which is free from the effect of downstream bottlenecks and experiences recurrent congestion during the peak hour. This requirement is to make sure to obtain freeway capacity at nonincident conditions under free flow condition. A collection site may be several miles long, depending on the extent of congestion, and would likely encompass several merge and d iverge areas Moreover, w ide geographic coverage within North America was attempted, to take into consideration the geographic effect on capacity and breakdown characteristics under incident conditions. Based on these criteria, several sites are selected, which are Interstate 15 SB that is located in San Diego, California, Interstate 5 NB that is located in Sacr a mento, California, etc. T he geographic characteristics location s of loop detectors and types of data available at each site are described below The formats of data at each site are attached in Appendix A. Interstate 15 SB is located in San Diego, California. The selected road section is from Balboa Avenue to I 52 with length of 2.42 miles. There are altogether 7 mainline detect ors and 5 ramp detectors in this section The configuration of the detector locations is illustrated in Figure 3 1. The most upstream detector is 1115802 and the most downstream detector is 1115779. The data collection period was from December, 2006 to November, 2007 ( https://pems.eecs.berkeley.edu/ ). There are about 106 days

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80 with incidents during the PM period through the data collection time at this site. The incident data includes information about the date, location, start time, duration, and causes of the incidents. Information on the number of lanes closed by incidents is not available. Interstate 5 N B is located in Sacramento California. The selected road section starts from Laguna Blvd to W. st with a length of about 10.41 mi les. There are totally 16 mainline detectors along this section. The configuration of the detectors is illustrated in Figure 3 2 The data collection period was from November, 2006 to November, 2007. There are about 220 days with incidents during the AM period through the data collection time at this site. The incident data includes information about the date, location, start time, duration, and causes of the incidents. Information on the number of lanes closed by incidents is not available. Que en Eliza beth Way ( QEW, Toronto, Canada) The selected road section is about 6.5 miles and consist s of four interchanges, which are Cawthra Road interchange, Hurontario Street interchange, Mississauga Road interchange and Southdown road interchange The most downst ream interchange, the Cawthra Road interchange, was found to be free from downstream congestion and considered to be the bottleneck The speed limit is 60 mi/h. A schematic of the section and t he location of detectors are shown in Figure 3 3 and 34 The d ata are collected from the ICAT (ITS Centre and Testbed) platform website developed by Simon Foo at the University of Toronto. The data collection period was from January, 2005 to December, 2005. The metering control period is 6:00:00 AM 10:00:00 AM. There are

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81 about 294 incidents through the data collection time at this collection site. The incident data includes information about the date, location, start time, and causes of the incidents. Information on the number of lanes a ffected by incidents is av ailable. US 217 SB, Portland, Oregon US 217 southbound is a 7mile corridor that serves commuters during peak periods between downtown Portland and suburban areas in Beaverton, Tigard, Lake Oswego, etc. It diverges from US 26, intersects with Highways 8 (Canyon Rd.), 10 (BeavertonHillsdale Hwy), 210 (Scholls Ferry Rd.), and 99W (Pacific Hwy), and finally merges onto I 5 southbound. A schematic of the section and t he location of detectors are shown in Figure 3 5 and Figure 3 6 This freeway corridor contains 12 onramps, 10 of which are controlled by ramp meters. The ramp metering system on this freeway is supported by 36 loop detectors and 9 CCTV cameras, and uses the strategy SWARM since early November 2005. The data collection period was from Jan 200 6 to July, 200 6 and Nov 2007 to Dec 2007. The incident data includes information about the date, location, start time, duration, type, and causes of the incidents. Information on the number of lanes affected is also available. Interstate 494 EB, Minne apolis Interstate 494 EB is located in Minneapolis The selected road section is about 3 miles in length, from Bass Lake Rd to Rock Ford Rd. The locations of detectors are shown in Figure 37 The data collection period was from September 200 6 to August 2007. There are about 930 incidents occurring through the data collection time at this site. The incident data includes information about the date, location, start time, and clear time of the incidents. Information on the number of lanes affected is also available.

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82 Methodology This sub chapter presents data analysis procedure. Data Screening To guarantee the quality of data and accuracy of analysis, t he collected data are screened in three aspects before further analysis, which are weather condition, incident condition and data quality. Firstly, d elete days with bad weather conditions to eliminate the impact of weather on capacity and traffic flow. Secondly, classify the data into several categories according to the time and location of incidents: condition with no incident incidents occurring before congestion condition, incidents occurring during congested period condition, and incidents occurring downstream condition. T hirdly, data with poor loop detector performance are removed from the dataset. (1) Weather Condition Loop detector data are screened for bad weather days through the weather forecast obtained from local weather station. Days with bad weather conditions ar e excluded from the dataset. This is because adverse weather decreases the capacities and operating speeds on freeways, and thus will affect the accuracy of the data analysis result s. Previous research show that severe rain and snow cause the most signifi cant reductions in capacities and operating speeds. The HCM 20 1 0 addresses the impact of adverse weather on freeway capacity The reported reductions in capacity caused by heavy snow are 19.527.8 %. The reported reductions in capacity caused by heavy rain are 10.7 % 17.7 %. Agarwal et al. (2005) concluded from four years data analysis that heavy rains (more than 0.25 inch/hour) and heavy snow (more than 0.5 inch/hour)

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83 reduce capacity by respectively 10% 17% and 19% 27%, and reduce speed by respectively 4% 7 % and 11% 15%. Generally, these values are significantly lower than those specified by the H CM 2000. They also found that even trace, light snow cause 3% 5%, 7% 9% reduction in speed and 3% 5%, 6% 11% reduction in capacity. In a word, adverse weather condi tion leads to different traffic flow performance compared to the clear weather. Thus, nearly all traffic engineering guidance and methods that are used to estimate highway capacity assume clear weather conditions (Agarwal et al., 2005). In this dissertati on, adverse weather is viewed as: Rain fall > 0.20 inch/day, or/and There is snow dropping during the day, or/and There is heavy fog, hail, blowing snow and tornado condition s (2) Incident Condition After the screening of adverse weather data, traffic data at the same site are separated into two categories: without incident s and with incident s occurring. Data with incidents and some data with no incident (selected to be close to the date of incidents) are kept for further analysis. Moreover, i ncidents are grouped into three categories by time and location: incident s occurring before congestion, incident s occurring during the congested period and incident s occurring downstream of the study site. Each category could be further classified by occurring at the bottleneck and nonbottleneck locations. (3) Data Quality Good quality data is important for freeway traffic control algorithms and analysis. There are many data screening criteria in previous research. For example, Cleghorn et

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84 al. (1991) screened the data, which were co llec ted from the Queen Eli z abeth Way (QE W ) in Ontario, Canada, based on the following criteria: a) volume must not be negative and must not exceed 60 vehicles per interval; b) Occupancy must not be negative and must not exceed 100 percen t; c) Speed must not be negative and cannot exceed 150 km/h (93 mph) The screening test is performed every interval (30 seconds) and a flag is set to mark the invalid datum once any of the tests failed. For data collected for this dissertation, a flag value exists in the data, which identifies the quality of the data. When the value of the flag is 0, then the data collected is good in quality. Otherwise, the data is not good. Therefore, data with the flag value nonzero are viewed to be bad and excluded f rom the dataset. Moreover, some websites have pointed out which detectors may be bad functioning during which time period. This may also help remove the bad quality data. Incident Verification In most of the cases, the reported incident time was a few minutes later than the actual incident time. Moreover, sometimes an incident may have no or little influence on traffic flow due to the demand, time and incident characteristics Thus it is necessary to verify the actual time, location and impact of incidents from various sources. These verification s are important to the accuracy of incident analysis, and can help avoid unnecessary analysis of minor incidents. Based on the literature review, this dissertation v erified the incidents from occupancy, speed, and the timeseries plots of speed and flow. If there was obvious occupancy and speed change caused by the incident, and if there were large change in the time series plots pattern, the incident was then considered to be significant in effect and kept for further analysis. Otherwise, the data would be removed.

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85 As it is difficult to distinguish incident induced congestion from recurrent congestion, the differences between occupancy changes caused by incidents an d that caused by congestion should be applied in verifying incidents. Firstly, apart f ro m occupancy, it also need to check the flow and speed during the incidents. Usually, incidents may cause a short period occupancy increase relative to recurrent congest ion. Secondly, check the occupancy upstream and downstream of the incident location. When an incident occurs, occupancy will increase at the upstream location and decrease at the downstream location. While when congestion experienced, occupancy will propag ate from the downstream bottleneck to upstream, and there is usually no much decrease in occupancy at the downstream locations. Based on the data analysis, an incident that is verified to affect traffic has the following characteristics : Occupancy immediately upstream of the incident location is greater than 20 percent: occi > 20 ; Occupancy immediately downstream of the incident location is less than 10 percent: occi+1 < 10 (except for incidents occurring at or downstream of the most downstream detector location, as there is no downstream data collected); The change in occupancy and speed lasts more than 10 minutes. An example from data of January 28, 2005 at the preliminary data analysis site is illustrated to show the verification proces s of incidents. On January 28 2005, the incident log indicates that there was a collision occurring at 15:05 at Cawthra Rd (downstream of detector 480DES). Time series plot of occupancy is made around 15:00 at the detector 480DES as well as the upstream detector 470DES and the downstream detector 500DES, as shown in Figure 38 A) It shows that when the incident occurs, occupancy at the upstream detector (470DES and 480DES) generally increase from

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86 10% to 50%, while occupancy at the downstream detector (500D ES) decreases from 10% to about 4%. Moreover, occupancy at the detector just upstream of the incident location i.e., 480DES, increases earlier and also ends earlier than 470DES. Figure 38 B ) describes the time series flow and speed plots at detector 480D ES. It shows that, there was congestion at 15:00 15:55 caused by the incident. The speed and flow dropped sharply to a very low level during the incident and recovered to a higher level after the incident. Thus, the incident was verified to occur at 15:00 15:30 downstream of the detector 480DES, and that it has effect on traffic flow. Data Analysis Procedure D ata are analyzed through the following procedure, (1) All the data are firstly screened for weather and data quality. Secondly, the time, location and effects of incidents are verified from occupancy, speed, and time series plots. For incidents verified to disrupt traffic, the speed, occupancy, and flow as we ll as their variances at the beginning of incidents are compared. The impact of incidents on operational conditions is analyzed from timeseries plots and density maps. (2) Define breakdown occurrence criteria. In this dissertation, a breakdown is defined as five or more consecutive 1minute intervals with speeds drops by 10 mph. This was established based on the time series speed plots at each detection location for several days. The breakdown is viewed to be activated if the following three criteria are met (Elefteriadou et al., 2009). i. Speed differences between two consecutive minutes is negative: 01 i i iS S S ii. The average speed during the previous 5 minutes is greater than the average speed in the following 5 minutes by at least 10 mph (or 16 km/h): mph S S Avg S S Avgi i i i10 ,..., ,...,4 1 5 iii. The maximum speed during the following 10 minutes (default value) is less than the speed before the speed drop. 1 9,..., i i iS S S Max To avoid confusion, this dissertation names recurrent congestion as demandinduced breakdown, and the congestion caused by incidents as incident induced breakdown.

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87 (3) Analyze the relationship between incidents and beginning of congestion. Further investigate the potential of developing a probabilistic incident induced breakdown model. (4) A definition and measurement of freeway capacity for incident conditions is proposed. Six parameters are proposed to define capacity for incident condition, which are respectively defined as, Maximum pre breakdown flow is the highest flow that occurred within 10 minutes before the breakdown or incident induced breakdown during non congested conditions. Breakdown flow is the one minute flow per lane for the interval before the demand induced breakdown or incident induced breakdown (i.e., before the speed drops by 10 mph for 10 minutes). Average flow for 10 minutes before breakdown is the average of ten minutes flow per lane before the breakdown. Average discharge flow during entire congestion is the average flow per lane during the congested conditions. Average discharge flow during both incident and congestion is the average flow per lane during both the incident conditions and congested conditions. Minimum 10 minute flow rate is the minimum 10 minute flow rate by lane (by moving average of ten successive 1 minute flows to reduce variation) measured in the bottleneck created by an incident. (5) Investigates the relationship between incident probability and operational conditions. Observations from the preliminary data analysis will be used in this step. Database Overview This sub section presents an overview of the data base The number of days of data analyzed for the diss ertation is summarized in Table 32 by different traffic conditions and locations.

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88 Table 3 1 Descri p tion of data available Site State Length (mi) Traffic d ata Weather d ata Incident d ata Volume Occ. Speed Start t ime Incident d uration # Lanes a ffect I 15 SB San Diego, CA 2.4 Y Y N Y Y Y N I 5 NB Sacramento, CA 10.4 Y Y N Y Y Y N QEW Toronto, Canada 6.5 Y Y Y Y Y N Y US 217 SB Portland, OR 7 N Y N Y Y Y Y I 494 EB Minneapolis, MN 3 Y Y Y Y Y Y Y Table 3 2 Summary of data analysis # Data p oints (days) Data with no incident Incident before c ongestion Incident during c ongestion Incident downstream Sum at 'B' at 'O' at 'B' at 'O' at 'B' at 'O' at 'B' at 'O' Toronto 56 0 7 4 1 8 4 0 80 Minne apolis 34 3 4 12 0 5 1 0 59 Portland 30 3 12 8 8 5 1 0 67 San Diego 73 0 4 1 6 1 2 0 87 Sacramento 65 10 2 11 1 6 0 4 99 Sum 258 16 29 36 16 25 8 4 392 B indicates bottleneck location, O indicates other locations.

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89 1115802 1115779 Figure 3 1 Location of detectors at I15 SB Direction of travel 314968314967 314792314934314936 314922314923 314780314910314909314896 314899 314768 314886314885 314867314876 313159 312133311847 Figure 3 2. Location of detectors at I5 NB 2252 380 370 2301 2302 2303 2251 2253 Southdown Rd 400 390 420 410 450 490 Figure 3 3 Schematic of detectors at the Que en Elizabeth Way ( QEW ) Site

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90 QEWDE0510DES Direction of travel QEWDE0500DES QEWDE02901ER QEWDE02801ER QEWDE0480DES QEWDE0470DES QEWDE02701ER QEWDE02601ER QEWDE0440DES QEWDE0450DES QEWDE02501ER QEWDE02401ER QEWDE0430DES QEWDE0390DES QEWDE0380DES QEWDE0370DES QEWDE02301ER QEWDE02251ER Figure 3 4. Location of detectors at QEW Figure 3 5 S chematic of the Portland site I Greenburg Direction of travel H Scholls Ferry F Denney E Allen D B-H Hwy C Walker G Hall J HWY99 A Barnes Figure 3 6. Location of detectors at the Portland site From US26E Barnes Rd. US26W Wilshire Rd. Walker Rd. B H Hwy Allen Blvd. Denney Rd. Hall Blvd. Scholls Ferry Rd. Greenburg Rd. Pacific Hwy 72nd Ave. Travel DirectionTo I 5 southbound N 0.1 0.45 0.76 1.92 2.55 3.12 3.5 4.35 5.11 5.95 6.77 0.1 0.45 0.76 1.92 2.55 3.12 3.5 4.35 5.11 5.95 6.77 Milepost

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91 Bass Lake Rd. Rockford Rd. Direction of travel 702 706 705 704 703 708 707 Figure 3 7 Location of detectors at the Minne apolis site A B Figure 3 8 Verification of incident on Jan 28, 2005 A) Chang in occ upancy and B) Change in flow 0 10 20 30 40 50 60 7014:45 14:50 14:55 15:00 15:05 15:10 15:15 15:20 15:25 15:30 15:35 15:40 15:45 15:50 15:55 16:00 16:05 16:10 16:15 Jan 28 2005 occupancy change with incident at 15:05 470 DES 480 DES 500 DES 0 10 20 30 40 50 60 70 80 0 1000 2000 3000 4000 5000 6000 700014:45 14:50 14:55 15:00 15:05 15:10 15:15 15:20 15:25 15:30 15:35 15:40 15:45 15:50 15:55 16:00 16:05 16:10 16:15Jan 28 2005 480DES with incident at 15:05 volume speed

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92 CHAPTER 4 QUALITATIVE ANALYSIS OF THE IMPACTS OF IN CIDENTS ON OPERATION AL CONDITIONS Methods often used in freeway bottleneck analysis include timeseries plots, density maps, and cumulative curves of vehicle counts (N curves). This chapter analyzes the impacts of incidents on operational conditions qualitatively based on the first two types of analysis. Th e third method is not considered, as the N curve method is vulnerable to the accumulation of errors resulting from biased counts and its contribution is modest when compared with that of careful speed analysis as reported by Kurada et al. (2007). For freeway segments with many onramps and off ramps, errors in vehicle counting are difficult to avoid due to reasons such as unstable detector performances. Thus the N curves at complex freeway bottlenecks would not be the best approach. This qualitative analy sis can provide a general idea and insights on achieving the stated objectives. Time series Plots This subchapter analyzes the relationship between incidents and the beginning of congestion. (1) C onditions with no incident Traffic data from January 12, 2005 at the Toronto site is used as an example of condition with no incident as shown in Figure 41. Figure 4 1 A) describes the change of occupancy around congestion: occupancy increases earliest at the most downstream detector 510DES and then at the upstre am detectors. Figure 41 B ) describes the change of speed at the beginning of congestion. A speed drop of 12 mi/h is observed firstly at the detector 510DES at 6:20 AM. These observations indicate that the location of the most downstream detector 510DES is the bottleneck. When comparing Figure A )

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93 and B ), change in speed is relatively larger than the change in occupancy at the beginning of congestion. Figure 4 1 C ) shows the flow and speed before, during, and after congestions from 6:2211:05 at the breakdown location Similar patterns in the time series plots exist during other recurrent congested periods. Breakdown starts at the bottleneck usually during AM peak periods. When breakdown occur s, speed drops first at the bottleneck location. C ongestion propagates to upstream detectors thus, congestion at the upstream detectors starts later and ends earlier. (2) Incident s occurring before congestion Traffic data from March 9, 2005 at Toronto site is used as an example of incidents occurring before congestion conditions. The incident log indicates that there is an incident occurring just downstream of the detector 480DES at 17:32. Thus, data at the detector 480DES, the upstream detector 470DES and the downstream detector 500DES are analyzed. There is no breakdown during the PM peak period this day. Figure 42 A ) shows that the occupancy upstream of the incident location (470DES, 480DES) increases from about 10% to 50%, while occupancy downstream of the incident location (500DES) decreases from a bout 10% to 5%. This is different from the change of occupancy at the beginning of congestion for condition with no incident during which the downstream occupancy does not change much. Figure 42 B ) shows that the speed upstream of the incident location ( 470DES, 480DES) decreases from about 65 mi/h to 10 mi/h, while speed downstream of the incident location (500DES) increases from about 65 mi/h to 75 mi/h. Occupancy and speed change earliest at the

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94 detector 480DES, e.g., there is a speed drop of 20 mi/h a t 17:17 at 480DES. Thus, the incident was observed to be at 480DES during 17:1718:01. Figure 42 C ) shows the speed and flow at the detector 480DES before, during, and after the incident. It is observed that there is congestion caused by the incident at 4 80DES during 17:1818:49. There are t wo operational conditions caused by the incident during congestion: during both incident and congestion (17:1718:01), after incident and during congestion (18:0118:49). The average flows during the two operational conditions are respectively 899 veh/h/ln and 1835 veh/h/ln. The average speeds during the two operational conditions are 9.4 mi/h and 36.9 mi/h. In summary, changes in flow and speed caused by incidents are much steeper than that caused by congestion, and last a relatively short period of time. (3) Incident s occurring during the congested period Traffic data from Oct 6, 2005 at Toronto site is used as an example of incidents occurring during congested conditions as shown in Figure 43 The incident log indicates that there is an incident occurring just downstream of the detector 440DES at 8:12. Thus data at the detector 440DES, the upstream detector 420DES and the downstream detector 460DES are analyzed. Figure 43 A ) shows that the occupancy upstream of the incident location (420DES, 440DES) increases from about 30% to 60%, while occupancy downstream of the incident location (460DES) decreases from about 30% to 5%. Detector 440DES is the first to show an increase in occupancy at 7: 5 8. Figure 43 B ) shows that the speed upstream of the incident location (420DES, 440DES) decreases from about 25 mi/h (already in congestion) to 8 mi/h, while speed downstream of the incident location

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95 (460DES) increases from about 25 mi/h to 65 mi/h. Detector 440DES first shows a speed drop of 14.5 mi/h at 7: 5 8. Based on the observation from Figure 43 A ) B ), the incident was verified to be at 8:028:38 at detector 440 DES. There is breakdown at the bottleneck 510DES at 6:33. C ongestion propagates to the upstream detector 440DES at 6:37, and recovers at 9:43. Figure 43 C ) shows time series plots of speed and flow immediately upstream of incident location at 440DES. Speed and volume drop sharply after the incident. The average discharge flow was 485 veh/h/ln during the incident, while 1709 veh/h/ln after the incident (during the congested period). The average speed was 9.2 mi/h during the incident, while 25.2 mi/h after the incident. From this viewpoint, the incident aggravated the conges tion. (4) Incident s occurring downstream of the bottleneck Traffic data from Sep 19, 2005 at Toronto site is used as an example of incidents occurring downstream of the bottleneck. The incident log indicates that an incident occurs at 12:29 at Dixie Rd (downstream of 510DES). Thus data at detector 510DES, and at the upstream detectors 500DES and 480DES, are analyzed. There is no downstream detector data available. Figure 44 A ) shows that occupancy increases greatly after the incident at all the detectors (all upstream of the incident). Figure 44 B ) shows that detector 510DES has a speed drop of 55 mi/h first after the incident at 12:27. Figure 44 C ) shows the timeseries plots of flow and speed at the detector 510DES, which indicates that there is congestion caused by the incident from 12:2713:25. The beginning of congestion for incidents occurring downstream conditions has similar pattern to that for incidents occurring before congestion condition, except that

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96 the impact of incidents on operations might be mitigated by the distance of the incidents from the bottleneck. (5) Minor Incidents Some incidents are identified to have little effect on traffic flow. They may cause the upstream occupancy increasing for a short time period, but not effective e nough to cause or aggravate congestion. In this case, flow and speed immediately upstream of the incident location may drop sharply for a short period of time, however, the impact on flow at further upstream detectors is little. Data of November 8, 2005 at Toronto site is used as an example. The incident log indicates that an incident occurs at 21:18 near the detector 510DES The i n cident was observed to be at 510DES at 21:1921:31 based on the change of occupancy and speed, as shown in Figure 45 A ) and B ). Figure C ) sho w s that, when the incident occurs, the average speed at 510DES drops to 17 mi/h and the average volume drops to 723 veh/h/ln H owever, the disruption in traffic flow only lasts 13 minutes. Conclusions Related to the Time Series Plots The nu mber of days examined, the start time and duration of c ongestion under nonincident and various incident conditions are summarized in Table 4 1 The third column provides the number of days for each condition. The fourth column provides the range of incident duration. The fifth column indicates that the start time of congestion is different for non incident and incident conditions: congestion might occur at any time through the day for incident conditions while is concent rated in the peak periods for non incident conditions. The sixth column indicates that the congestion durations for

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97 incidents occurring before congestion and downstream of the bottleneck are relatively shorter than the other two conditions. A comparison of the changes in operational conditions for normal (5 minute before and after breakdown) and incident conditions (5minute before and after incident) are summarized in Table 4 2. The distributions of the changes for non incident and incident conditions are illustrated in Figure 46. Operations can be classified into four states by the time and duration of incidents: before congestion (10 minute), during incidents and congestion, after incidents and during congestion, post congestion recovery (10minute). The average values of flow, speed, and occupancy during different operational states for various incident conditions are respectively shown in Column 3 to Column 6 in Table 43. San Diego and Sacramento sites have few crashes verified and thus are not include d in Table 4 3 Six conclusions on the impact of incidents on operational conditions are drawn: (1) Demandinduced breakdown starts at the bottleneck usually during the AM peak periods. When breakdown happens, congestion propagates to upstream detectors, thus congestion at the upstream detectors starts later and ends earlier. (2) Incident induced breakdown might occur at both bottleneck and non bottleneck locations, during the peak and off peak periods. Detectors immediately upstream of the incident location are the first to show an abrupt increase in occupancy, while detectors immediately downstream show a decrease in occupancy, similar to the observations made by Shaik (2003) and Masinick and Teng (2004). (3) Apart from occupancy, speed can also be used in verifying incidents. Detectors immediately upstream of the incident location are the first to show an abrupt decrease in speed, while detectors immediately downstream show an increase in speed. Changes in speed at the beginning of congestion are relatively more obv ious than the changes in occupancy. (4) Changes in operational condition at the beginning of congestion are much steeper for incident conditions than for non incident conditions. For instance, at the Toronto site, the average 5minute changes in flow, speed, and occupancy before/after incidents are respectively 31%, 6 5 %, and 218 %; while the average

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98 5 minute changes in flow, speed, and occupancy before/after congestion (for non incident conditions) are respectively 3 %, 3 2 %, and 32%. (5) Comparing the 10minut e operations before congestion with the 10minute operations after recovery ( as shown in Table 43), there is not much difference between the average speed and occupancy. However, average flow 10minute before congestion is generally much higher than the average flow 10minute after recovery. (6) Comparing congested conditions during/after incidents ( as shown in Table 43), incidents aggravated the congestion. Take the Toronto site as an instance, t he average flow, occupancy, and speed during incidents and cong estion are around 9 5 0 veh/h/ln, 40 and 1 6 mi/h; The average flow, occupancy, and speed after incidents and during congestion are around 1700 veh/h/ln, 25 and 35 mi/h. Density Maps Shock wave analysis is usually used in travel time estimation and travel demand analysis, and might be used in estimating incident duration. This subchapter compares the density maps under nonincident and different types of incident conditions to illustrate the impact of incidents on congestion propagation. Density is calculat ed based on the occupancy detector length and vehicle length using equation 41: OCC OCC L L kD v% 6 18 8 52 % 8 52 (Eq. 4 1) W here, the vehicle length vL and detector length DL are respectively 18 feet and 6 feet. The calculation time step is every 5 minute or 1 minute, according to the duration of incidents and congestion. Flow with density less than 40 vehicles per lanemile is viewed to be uncongested flow, flow with density between 40 and 65 is viewed to be unstable flow that is near capacity flow condition, while flow with density greater than 65 is viewed to be congested flow ( May 1990). Density maps are only plotted for the Toronto site, as Minneapolis and Portland sites have two or more than two bottlenecks with one in the middle of the road section,

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99 which make it difficult to identify the reason of congestion. In the density maps below, the horizontal axis are the detectors along the travel direction with 510DES or 480DES as the bottleneck, the vertical axis is time. A five star indicates the location and start time of an incident. Shock waves are viewed to be the density curves of 65 vehicles per lanemile. (1) C ondition with no incident Data of February 10, 2005 is used as an example of condition with no incident There was breakdown at 6:3110:59 at the bottleneck (detector 510DES). Figure 47 shows that the shockwave forms a regular pattern with mainly three shockwaves: a frontal stationary shockwave at the bottleneck, a backward forming shock wave, and a forward recovery shockwave. The highest densities were only little above 100 and occur at only few detector locations. The conges tion propagates to the most upstream detector 370DES at 7:25, taking 49 minutes. The distance between 370DES and 510DES is about 10.25 km. T h us, the speed of the shockwave is 7.8 mi/h. (2) Incident s occurring before congestion Data of March 9, 2005 and May 25 2005 are used as examples of incidents occurring before congestion conditions, as shown in Figure 48 and 49. On March 9 2005, an incident occurr ed downstream of the detector 490DES at 17:1718:01, and caused incident induced breakdown at 17:1818:03. O n May 25 2005, an incident occurr ed downstream of the detector 440DES at 9:5710:26, and caused incident induced breakdown at 9:5910:27. It is observed from Figures 48 4 9 show that the frontal stationary shock wave occurred immediately upstream of the incident locations

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100 but not at the bottleneck, and that the shock wave recovers shortly following the clearance of the incident Contrary to the nonincident conditions, density downstream of the incident location is very low during the study period, and the highest density (greater than 100) appeared at more detector locations. The speeds of shockwaves are calculated. On March 9, congestion propagates to the most upstream detector 370DES at 17:59, taking 42 minutes. The distance between the incident location 480DES and 370DES is about 7.8 km. T h us, the speed of the shockwave is 6.9 mi/h. On May 25, congestion propagates to the most upstream detector 370DES at 10:16, taking 19 minutes. The distance between the incident location 440DES and 370DES is about 4.8 km. T h us, the speed of the shockwave is 9.5 mi/h. (3) Incident s occurring during the congested period Data of October 6, 2005 is used as an example of incidents occurring duri ng congested period conditions. There is congestion at 6:379:43 at the most downstream detector 510DES. An incident occurred at 8:028:38 at detector 440DES. Figure 410 shows that the shockwaves have similar shape as that for non incident conditions (Fig ure 47). However, during the incident, upstream density increased greatly while downstream density decreased sharply. The highest densities are high above 100 while the lowest densities approaching 5. Figure 411 illustrates the change in density during the incident in detail with 1minute time step. The shockwave with density greater than 100 propagates to the most upstream detector 370DES at 8:11, taking 9 minutes. The distance between the incident

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101 location 440DES and the location at 370DES is 4.83 km. The speed of the shockwave is 16.4 mi/h. (4) Incident s occurring downstream Data of September 22, 2005 is used as an example of incidents occurring downstream, as shown in Figure 412. There was an incident occurring at 17:16 19:46 downstream of the most downstream detector 510DES. Figure 412 shows that the shockwaves cover relatively a small area. The two downstream detectors 510DES and 500DES have almost the highest density with the longest duration. Congestion propagates to the upstream detector 380DES at 17:40, taking 25 minutes. The distance between the incident location 510DES and the location at 380DES is 9.33 km. The speed of the shockwave is 13.9 mi/h. Conclusions Related to Density Maps When congestion ( non incident conditions) or an incident begins, densities might change with time and are different at the upstream and downstream locations. Percentage changes in densities at the beginning of congestion or incidents at Toronto site are summarized in Table 44, based on analysis of the density maps illustrated above. Comparing the density maps for different conditions, s everal preliminary conclusions are drawn regarding the impact of incidents on congestion, (1) For nonincident conditions (e.g, see Figure 4 6), the density map forms a regular shape with mainly three shockwaves: a frontal stationary shockwave, a backward forming shock wave, and a forward recovery shockwave. The frontal stationary shockwave occur at the bottleneck. The highest densities were only little above 100 and occur at only few detector locations. (2) For incidents occurring before congestion (e.g, see Figures 47 and 48), the frontal shockwave moves from the bottleneck to the incident location. The shock

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102 wave usually recovers following the clearance of the incident. The highest density (greater than 100) appeared at more detector locations. (3) For incidents occurring during congested period (e.g, see Figure 49), the shockwaves have similar shapes to that at non incident conditions. However, during the incident, density upstream of the incident location increased greatly while density downstream decreased sharply. The highest densities are high above 100 forming a rectangle, with the lowest densities approaching 5. (4) For incidents occurring downstream (e.g, see Figure 410), the shockwaves concentrate at the most downstream detectors and have a relatively smaller range, probably due to the distance between the incident location and the bottleneck. (5) The 5 minute changes in density caused by incidents ( 36.45%) are larger than that caused by recurrent congestion ( 10.32%) ( as shown in Column 3 of Table 44). The downstream densities decrease by 76% when incidents occur, while do not have change under nonincident conditions. However, these observations are based on a limited amount of data poi nts. (6) Based on the analysis of density maps illustrated above, the speeds of shockwave are 7.8 mi/h and 6.4 mi/h for nonincident conditions, 6.9 mi/h and 9.5 mi/h for incident occurring before congestion conditions, 16.4 mi/h for incidents occurring during congested period conditions, and 13.9 mi/h for incident occurring downstream conditions. Generally, the speeds of shockwave for incident conditions are larger than that for nonincident conditions. However, these observations are based on a limited amount of data points. Conclusions A qualitative analysis of the impact of incidents on operational conditions is conducted through time series plots and density map. Speed seems to be more appropriate than occupancy in incident verification. There is reduction in discharge flow caused by incident s. Generally, the speed of shockwaves for incident conditions is larger than that for nonincident conditions. It is suggested that comparing the changes in operational conditions at the beginning of congestion for non i ncident and incident conditions can help predict the probability of incidents and incident induced breakdown.

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103 Table 4 1 R elationship between i ncident s and beginning of congestion Site Type of d ata # Days Incident d uration r ange (min) Start t ime of congestion Congestion d uration r ange (min) Toronto No incident 56 N/A 5:47 7:31 62 360 (18 2 )* Before c ongestion 1 1 1 6 8 0 (3 5 ) 6:30 19 :30 1 9 266 ( 7 1 ) During c ongestion 9 25 41 (32) 6:30 16:00 56 237 (1 53 ) Downstream 4 25 59 ( 36 ) 9:45 22:30 26 58 ( 36 ) Minneapolis No incident 35 N/A 6:50 7:51 9 138 (67) Before congestion 16 12 83 (42) 5:40 18:30 22 107 (51) During congestion 5 31 62 (44) 6:50 8:05 35 121 (72) Downstream 1 77 8:13 78 Portland No incident 33 N/A 14:38 16:29 54 385 (17 3 ) Before congestion 2 0 20 91 (4 7 ) 3:44 19:00 2 4 1 1 7 ( 63 ) During congestion 1 3 20 104 (4 2 ) 7:20 19:00 37 328 (1 36 ) Downstream 1 58 8:06 75 Note: Indicates the average value. Table 4 2 Changes in o perational conditions 5min before/after b reakdown or 5min before/afte r i ncidents Percent changes Flow Speed Occ No incident I ncident No incident I ncident No incident I ncident Min 28.00% 90.00% 17.00% 19.00% 92.00% 1761.00% Toronto Av g. 3.48% 31.68% 32.44% 64.85% 46.13% 217.71% Max 21.00% 65.00% 53.00% 89.00% 21.00% 32.00% Min 13.00% 34.83% 18.82% 11.34% 174.75% 539.47% Portland Av g. 8.76% 32.60% 35.20% 54.43% 54.07% 158.85% Max 51.68% 100.00% 65.76% 100.00% 17.51% 100.00% Min 25.40% 15.99% 24.32% 12.90% 131.60% 295.73% M inneapolis Av g. 11.32% 21.69% 46.17% 46.00% 73.43% 98.10% Max 36.45% 64.43% 66.12% 87.26% 57.36% 30.93%

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104 Table 4 3 Operational conditions during different states at each data collection sites. (Units: flow veh/h/ln, occ %, speed mi/h). 10 min before congestion D uring incident & congestion A fter incident & during congestion 10min post recovery av g flow av g occ av g speed av g flow av g occ av g speed av g flow av g occ av g speed av g flow av g occ av g speed Toronto N o incident 2040 17 60 N/A N/A N/A 1865 29 34 1797 17 59 incident before 1799 11 66 985 36 20 1687 24 37 1624 13 57 incident during 1752 17 56 880 44 12 1711 26 35 1712 15 60 incident downstream 1407 16 67 946 47 17 N/A N/A N/A 1121 13 74 Minneapolis No incident 1881 19 64 N/A N/A N/A 1644 35 32 1639 18 59 incident before 1563 14 63 1131 36 22 1557 31 27 1629 17 57 incident during 1988 17 67 1125 33 22 N/A N/A N/A 1738 16 60 incident downstream 1650 16 68 1322 40 25 N/A N/A N/A 1443 13 71 Portland No incident 1859 13 55 N/A N/A N/A 1741 21 34 1709 12 54 incident before 1394 9 53 889 30 16 1382 22 26 1343 9 53 incident during 1697 11 54 789 38 14 1524 21 30 1477 10 58 incident downstream 2061 16 46 528 55 11 1075 33 24 1664 14 43 Table 4 4 Changes in density at the beginning of congestion or incidents at Toronto site % Change in density at ti+1 % Change in density at ti 1 % Change in density at upstream % Change in density at downstream No incident (#2) 1 min 8.67% 17.05% 35.32% 5 min 35.31% 10.32% 29.21% 0.00% Incident (#3) 1 min 21.80% 32.92% 34.59% 71.53% 5 min 34.46% 36.45% 11.80% 75.96%

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105 A B C Figure 4 1 Time series speed a nd f low p lots for condition with no incident A) Time series occupancy, B) Time series speed, and C) Time series flow and speed before, during and after congestion. Jan 12 2005 time series occupancy during normal condition 0 10 20 30 40 50 60 6:10:0 6:12:0 6:14:0 6:16:0 6:18:0 6:20:0 6:22:0 6:24:0 6:26:0 6:28:0 6:30:0 6:32:0 6:34:0 6:36:0 6:38:0 6:40:0 480 DES 500 DES 510 DES Jan 12 2005 time series speed during normal condition 0 10 20 30 40 50 60 70 80 6:10:0 6:12:0 6:14:0 6:16:0 6:18:0 6:20:0 6:22:0 6:24:0 6:26:0 6:28:0 6:30:0 6:32:0 6:34:0 6:36:0 6:38:0 6:40:0 480 DES 500 DES 510 DES Jan 12 2005 510DES breakdown at normal condition 0 1000 2000 3000 4000 5000 6000 7000 6:0:0 6:13:0 6:26:0 6:39:0 6:52:0 7:5:0 7:18:0 7:31:0 7:44:0 7:57:0 8:10:0 8:23:0 8:36:0 8:49:0 9:2:0 9:15:0 9:28:0 9:41:0 9:54:0 10:7:0 10:20:0 10:33:0 10:46:0 10:59:0 11:12:0 0 10 20 30 40 50 60 70 80 90 100 volume speed

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106 A B C Figure 4 2. Time series p lots for incidents occurring before breakdown (March 9, 2005) A) Time series occupancy, B) Time series speed, and C) Time series flow and speed before, during and after congestion. March 9 2005 time series occupancy with incident 0 10 20 30 40 50 60 70 17:15:0 17:18:0 17:21:0 17:24:0 17:27:0 17:30:0 17:33:0 17:36:0 17:39:0 17:42:0 17:45:0 17:48:0 17:51:0 17:54:0 17:57:0 18:0:0 18:3:0 18:6:0 18:9:0 18:12:0 18:15:0 470 DES 480 DES 500 DES March 9 2005 time series speed with incident 0 10 20 30 40 50 60 70 80 90 17:15:0 17:18:0 17:21:0 17:24:0 17:27:0 17:30:0 17:33:0 17:36:0 17:39:0 17:42:0 17:45:0 17:48:0 17:51:0 17:54:0 17:57:0 18:0:0 18:3:0 18:6:0 18:9:0 18:12:0 18:15:0 470 DES 480 DES 500 DES March 9 2005 480DES incident induced breakdown 0 1000 2000 3000 4000 5000 6000 7000 17:0:0 17:5:0 17:10:0 17:15:0 17:20:0 17:25:0 17:30:0 17:35:0 17:40:0 17:45:0 17:50:0 17:55:0 18:0:0 18:5:0 18:10:0 18:15:0 18:20:0 18:25:0 18:30:0 18:35:0 18:40:0 18:45:0 18:50:0 18:55:0 19:0:0 0 10 20 30 40 50 60 70 80 volume speed During incident A fter incident

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107 A B C Figure 4 3 Time series p lots for incident during the congested period (Oct 6, 2005) A) Time series occupancy, B) Time series speed, and C) Time series flow and speed before, during and after congestion. Oct 6 2005 time series occupancy with incident 0 10 20 30 40 50 60 70 80 90 7:45:0 7:48:0 7:51:0 7:54:0 7:57:0 8:0:0 8:3:0 8:6:0 8:9:0 8:12:0 8:15:0 8:18:0 8:21:0 8:24:0 8:27:0 8:30:0 8:33:0 8:36:0 8:39:0 8:42:0 8:45:0 420 DES 440 DES 460 DES Oct 6 2005 time series speed with incident 0 10 20 30 40 50 60 70 80 7:45:0 7:48:0 7:51:0 7:54:0 7:57:0 8:0:0 8:3:0 8:6:0 8:9:0 8:12:0 8:15:0 8:18:0 8:21:0 8:24:0 8:27:0 8:30:0 8:33:0 8:36:0 8:39:0 8:42:0 8:45:0 420 DES 440 DES 460 DES Oct 6 2005 440DES congestion with incident 0 1000 2000 3000 4000 5000 6000 7000 8000 6:30:0 6:39:0 6:48:0 6:57:0 7:6:0 7:15:0 7:24:0 7:33:0 7:42:0 7:51:0 8:0:0 8:9:0 8:18:0 8:27:0 8:36:0 8:45:0 8:54:0 9:3:0 9:12:0 9:21:0 9:30:0 9:39:0 9:48:0 9:57:0 0 10 20 30 40 50 60 70 flow speed After Incident

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108 A B C Figure 4 4 Time series p lots for incident occurring downstream c ondition (Sep 19, 2005) A) Time series occupancy, B) Time series speed, and C) Time series flow and speed before, during and after congestion. Sep 19 2005 time series occupancy with incident 0 10 20 30 40 50 60 70 80 9012:15:0 12:20:0 12:25:0 12:30:0 12:35:0 12:40:0 12:45:0 12:50:0 12:55:0 13:0:0 13:5:0 13:10:0 13:15:0 13:20:0 13:25:0 13:30:0 13:35:0 13:40:0 13:45:0 480 DES 500 DES 510 DES Sep 19 2005 time series speed with incident 0 10 20 30 40 50 60 70 80 90 10012:15:0 12:20:0 12:25:0 12:30:0 12:35:0 12:40:0 12:45:0 12:50:0 12:55:0 13:0:0 13:5:0 13:10:0 13:15:0 13:20:0 13:25:0 13:30:0 13:35:0 13:40:0 13:45:0 480 DES 500 DES 510 DES Sep 19 2005 510DES incident-induced breakdown 0 1000 2000 3000 4000 5000 6000 7000 800012:15:0 12:20:0 12:25:0 12:30:0 12:35:0 12:40:0 12:45:0 12:50:0 12:55:0 13:0:0 13:5:0 13:10:0 13:15:0 13:20:0 13:25:0 13:30:0 13:35:0 13:40:0 13:45:00 20 40 60 80 100 120 volume speed

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109 A B C Figure 4 5 Time series speed a nd f low p lots for minor incidents (Nov 8, 2005) A) Time series occupancy, B) Time series speed, and C) Time series flow and speed before, during and after congestion. Nov 8 2005 time series occupancy with incident 0 10 20 30 40 50 60 70 80 21:0:0 21:3:0 21:6:0 21:9:0 21:12:0 21:15:0 21:18:0 21:21:0 21:24:0 21:27:0 21:30:0 21:33:0 21:36:0 21:39:0 21:42:0 21:45:0 21:48:0 21:51:0 21:54:0 21:57:0 22:0:0 480 DES 500 DES 510 DES Nov 8 2005 time series speed with incident 0 10 20 30 40 50 60 70 80 90 21:0:0 21:3:0 21:6:0 21:9:0 21:12:0 21:15:0 21:18:0 21:21:0 21:24:0 21:27:0 21:30:0 21:33:0 21:36:0 21:39:0 21:42:0 21:45:0 21:48:0 21:51:0 21:54:0 21:57:0 22:0:0 480 DES 500 DES 510 DES Nov 8 2005 510DES with incident 0 1000 2000 3000 4000 5000 6000 21:0:0 21:5:0 21:10:0 21:15:0 21:20:0 21:25:0 21:30:0 21:35:0 21:40:0 21:45:0 21:50:0 21:55:0 22:0:0 0 10 20 30 40 50 60 70 80 volume speed

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110 A B C Figure 4 6. Distributions of the changes in operations for no incident and incident conditions. A) Changes in flow. B) Changes in speed. C) Changes in occ. (Note: T Toronto, P Portland site, M Minneapolis; N no incident condition, I incident condition) -100% -50% 0% 50% 100% 150% T-N T-I P-N P-I M-N M-I -50% 0% 50% 100% 150% 200% T-N T-I P-N P-I M-N M-I -1800% -1600% -1400% -1200% -1000% -800% -600% -400% -200% 0% 200% T-N T-I P-N P-I M-N M-I

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111 Figure 4 7 Density m ap of Feb 10 2005 without i ncident

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112 Figure 4 8 Density m ap of March 9 2005 with i ncident at 17:17 18:01 at 49 0DES

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113 Figure 4 9 Density m ap of May 25 2005 with i ncident at 9:57 10:27 at 440DES

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114 Figure 4 10. Density m ap of Oct 6 2005 with i ncident at 8:028:38 at 440DES (5 min)

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115 Figure 4 11. Density m ap of Oct 6 2005 with i ncident at 8:028:38 at 440DES (1 min)

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116 Figure 4 12. Density Map of Sep 22 2005 with Incident at 17:1619:46 at 51 0DES

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117 CHAPTER 5 FREEWAY CAPACITY UNDER INCIDENT CONDITIO NS Freeway capacity is an important metric that is used to evaluate the performance of a facility as well as to manage traffic operations. Freeway capacity under incident conditions is also an important metric, which can be used to optimize system performance in cases of such disruptions. In cident s may block one or more lanes and/or the adjacent shoulder lane. Previous research ( Goolsby, M. E. 1971 1, HCM 20 1 0 ) has estimated the capacity remaining after an incident based on the number of lanes blocked by the incident However, the literature has not reported on the relationship between freeway capacity and other incident characteristics (e.g., incident duration), incident type and geometric charact eristics Moreover, the literature has not produced any models relating the capacity before an incident to the capacity after an incident. Such a relationship could help estimate capacity under incident conditions more accurately, and can be used in incident management, queue estimation, etc. The objectives of this chapter are to: Extract and assess the capacity of freeway facilities under non incident conditions Compare values of capacity remaining after incidents to previous values reported in the liter ature Extract and analyze capacity under incident conditions Develop models to predict capacity as well as capacity reduction under incident conditions Data collected from all the five data collection sites are used in this chapter C apacity under N onincident C onditions This section provides the results of the analysis for estimating capacity under no n incident conditions. Data collected from all the five sites (as shown in Table 3 1 ) we re

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118 used. At each site, the range, average, and standard deviation of the four capacity parameters pertaining to non incident conditions were obtained using the procedure described above and are provided in Table 5 1 The table provides the weighted average (by the number of data points for each site) of each parameter f or 2 lane, 3lane, and 4lane sites. Figure 5 1 plots the four capacity parameters by the number of lanes As shown, all four parameters are the highest for threelane sections, and the lowest for five lane section. Statistic al analysis results indicate that all the four parameters are significantly higher (at 95% confidence interval) at threelane freeway than at other freeways. This suggests that threelane freeway s have a higher productivity in terms of vehicles per hour per lane than other freeway facilities. This is different from the HCM 2010, which does not address the relationship between freeway capacity and number of lanes. It is also different from the HCM 2000, which says that the per lane capacity of a freeway segment increases with the number of lanes Also, breakdown flow is generally higher than the average discharge flow for all the sites. A mong the four capacity parameters, breakdown flow has the largest range of values, while average discharge flow generally has the smallest range of values. It is also observed that t he capacities in Table 5 1 are lower than those mentioned in the HCM For example, the maximum prebreakdown flow ( 1 minute peak capacities ) is lower than the capacity of a basic freeway segment ( 15minute flows ) reported in the HCM 2010, which is approximately 2, 300 pc/h/ln under a FFS of 60 mi/h u nder base traffic and geometric conditions (the FFS of the data collection sites are all above 60 mi/h) The average discharge flow is much lower than t he queue discharge

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119 flow of 2,000 to 2,300 pc/h/ln as suggested in HCM 2000. One possible reason of the difference is that the capacity values shown in Table 5 1 are obtained at freeway bottlenecks, which are usually lower than that at basic freeway segmen t. The standard deviations of the capacity parameters are in the range of 50 to 250 (veh/h/ln). C apacity for I ncident C onditions This section defines capacity for incident conditions compares incident capacity measured using this database to the results of previous research, and presents models for estimating capacity and capacity reduction during incidents. Capacity under Incident Conditions Based on the literature review and data analysis, t his dissertation will evaluate two parameters in defining incident capacity: the average discharge flow per open lane when both incident and congestion are present, and the minimum 10minute flow rate when both incident and congestion are present. Of the five data collec tions sites, only data collected from three sites ( Minneapolis, Portland, and Toronto) are used to analyze capacity for incident conditions, as these were the only ones providing data on the number of lanes affected. T he number of lanes affected is not nec essarily the number of lanes closed throughout the incident, as this might vary throughout the incident. There are some cases when the number of lanes closed is equal to the total number of lanes of the facility, however, the flow for those cases is not zero. Also, the exact meaning of this variable might be different for different incidents and different sites. At the Portland site, the incident log records the number of lanes closed and there is detailed information about the number of lanes closed thr oughout the incident (the number of lanes closed may change throughout the incident). Thus, at the Portland site, an incident data point might be split into several

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120 data points which would be analyzed separately according to the variation of number of lanes affected throughout the incident. Apart from the number of lanes affected by the incident, the incident data also include the date, location, start time, duration (except for the Toronto site), and cause of the incident. Some other factors that might affect incident capacity are also collected, including incident category, congestion duration, speed limit, free flow speed, and peak hour factor, etc The relationship between parameters of incident capacity and the number of lanes open/ affected is illustra ted in Table 5 2 based on data analysis of the three sites. The number of lanes open is obtained as the difference between total number of lanes and number of lanes affected. As shown, the average flow per total lanes for incident conditions does not alwa ys follow the expected trends. For example, for a facility with no lane open, the average flow is higher when the shoulder is affected than when it is not! This likely occurs because the variable Number of lanes affected is not constant throughout the analysis period, and that pattern might also vary from incident to incident. The discrepancies are also likely attributable to sample size. The average flow per open lanes also provides a wide range of results, probably for similar reasons. As shown, its hig hest value is for 1 lane open conditions, and it is not much different for lanes open and 3 lanes open conditions T he results pertaining to the minimum 10 min flow rate are more reasonable, as this flow increases with the number of lanes open. However, there are some discrepancies with respect to the impact of shoulder closures. Generally, the values of the standard deviations of incident capacities are around 300.

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121 Table 5 3 compares the two parameters of incident capacity at the three sites by the number of lanes open. The table shows that, for all the sites, the average discharge flow per open lane when both incident and congestion are present is the highest for 1 lane open sites then for 2 lanes open sites and then for 0 lane open sites. This indicates that only a few vehicles can go through when all the lanes are affected, and that the open lane is used more productively when 1 lane is open than when 2 lanes are open. The minimum 10min flow rate increases with number of lanes open, except for the 2 lanes open and 1 lane open data at the Portland site. The reason might be that the total number of lanes are mostly 2 for 1 lane open data and are mostly 3 for 2 lanes open data at the Portland site, thus, the per lane flow at locations with three lanes are lower than that at locations with two lanes. It should be noted that for data along one lane open facilities, some of the flows per open lane are higher t han expected (above 2000 veh/hr/lane). This might occur, either because there are more than one lane for a portion of the time, or because more than one vehicle can pass through the incident area simultaneously. It is also observed from Table 5 3 that the values of the standard deviations of incident capacities are around 300 and higher than 500 for 1 lane open condition. Based on the observations provided above, i n this dissertation the capacity remaining after incidents is calculated in two ways. It is calculated as the ratio of the minimum 10min flow rate to the average discharge flow for non incident conditions (averaged for each site), and also as the ratio of the minimum 10min. flow rate to the 10min flow before breakdown for non incident conditi ons (averaged for each site). For

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122 comparison purposes, the capacity remaining after incidents under various conditions found by this chapter and previous research are provided in Table 5 4 Comparing the values shown in Table 5 4 based on the average discharge flow it is found that : For a 2 lane facility, the value of capacity remaining for shoulder affected is close to the values in previous research However, incident capacity for 1 lane affected and 2lanes affected conditions are much higher (by about 15 %) than that in previous research. For a 3lane facility, the value of capacity remaining for 1 lane affected is close to the values in previous research. However, incident capacity for 2lanes affected is higher (by about 10% 15%) than that in previous research. Comparing the values obtained by this chapter based on average flow 10min before breakdown with previous research, it is found that : For a 2 lane facility, the values of capacity remaining is lower by about 10% than previous research for should er affected conditions, and are higher by about 10% than previous research for 1 lane affected and 2lane s affected conditions For a 3 lane facility, the values of percent capacity remaining after incidents are similar to that by Smith et al (2003), but are different from other research by about 10%. A major reason for the differences in remaining capacity between previous research and this dissertation is probably that previous research (e.g., Smith et al 2003, Chin et al., 2004 ) use d the peak /maximum of the flowdensity curv e as capacity under prevailing nonincident conditions, while this dissertation uses the average discharge flow and the average flow 10min before breakdown for each site as the capacity under non incident conditions. Thus, the obt ained percent of capacity remaining after incidents in this dissertation might be higher. Another reason might be that the percent values obtained in this dissertation are based on the number of lanes affected by incidents. However in previous research, t he remaining capacity was

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123 estimated based on the number of lanes blocked by incidents. The discrepancies might also be due to the fact that incident capacities (mean the minimum 10min flow rate here) are variables with a large variance. As shown in Ta b le 5 2 and Table 5 3 the standard deviations of the minimum 10min flow rate are around 300 veh/h/ln which are larger than that of nonincident capacities ( 5 0 250 veh/h/ln, as shown in Table 5 1 ). Another difference from previous research is that this disse rtation analyzes capacity for shoulder plus one lane or two lanes affected conditions. Estimate of Capacity/Capacity Reduction under Incident Conditions Apart from the number of lanes affected/open, the effects of some other variables on the two parameters of incident capacity are also evaluated, as shown in Table 5 5 Table 5 5 show s that both parameters of incident capacity are much lower for incidents occurring during congested periods than for incidents occurring before congestion or downstream of the bottleneck. This is because for incidents occurring during congested periods, flows just prior to the incident are much lower than those for other condit ions. The minimum 10min flow is higher at locations with 2 lanes than at locations with 3 lanes. There is no clear pattern of the effects of the other three factors on the two parameters. It was also observed from scatter plots that, generally, the two parameters of incident capacity decrease slightly with incident duration However, the trend is small and variation is large. There seems to be no relationship between incident capacity and congestion duration. Thus, these variables are not used in the model development described below. A regression model was developed to estimate capacity under incident conditions, as well as capacity reduction during incidents.

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124 Based on the above observations, the factors incident duration, incident category, total number of lanes, the number of lanes open, and number of lanes affected, should be further explored in developing incident capacity estimation models. Factors such as incident duration were not found to be related to incident capacity in the data analysis proc ess, and thus are not included in the model. Data with 0 lane affected shoulder+1lane affected and shoulder+2 lanes affected which are mostly from the Portland site, are not used in the model estimation, as they have few data points (less than 10 points, as shown in Table 5 2 ). Preliminary analysis with these data points included was not as good. The two parameters of incident capacity were each used as the dependent variable, and i t was concluded that the models had a better fit when the minimum 10min flow rate is used The estimates of the parameters for minimum 10min flow rate are shown in Table 5 6 Us ing the total capacity reduction (uses average discharge flow as capacity for nonincident conditions and the minimum 10min flow as capacity for incident conditions), as the dependent variable, t he preliminary estimates of the parameters are shown in Table 5 7 In this case, the incident category, total number of lanes, and number of lanes aff ected are statistically significant at the 95% confidence interval. Based on the above analysis, the number of lanes open/ affected by incidents is found to be the most important factor that influences incident capacity. Another significant factor is incident category. Also, using the minimum 10min flow rate results in a better model, likely because it matches better the number of lanes affected. The estimated total capacity reduction is illustrated in the following equation,

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125 ected lanes..aff 77,..2 cted lane..affe 1172,..1 affected r ,..shoulde 008 2 1361 386 .. nlane inccate reduction capacity C onclusions and R ecommendations This chapter studies freeway capacity for both non incident and incident conditions. The following conclusions are drawn. Based on the data analyzed in this chapter t hree lane freeway s seem to be the most efficient in terms of per lane capacity for nonincident conditions. This finding is based on the observation that threelane freeway s had the highest four parameters of capacity (breakdown flow, etc), compared to twolane, four lane and five lane freeways. This differs from the HCM 2010 which does not address the relationship between freeway capacity and number of lanes, and differs from the HCM 2000 which indicates that per lane capacity increases with the number of lanes. T his finding is based on data collected from five freeways, and needs to be further explored with data from additional freeways. T wo parameters were identified for defining incident capacity: average discharge flow per open lane when both incident and congestion are present, and the minimum 10min flow rate during that same period. It can be concluded that the minimum 10min flow rate provides a better fit with the data as they are currently reported, because it correlates better with the maximum number of lanes affected. Apart from the number of lanes affected by incidents, the relationship between incident capacity and other variables was also examined. M ultiple linear regression model s were developed to estimate incident capacity and capacity reduction under incident conditions, based on parameters such as incident category, number of lanes

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126 open, and the number of lanes affected. Results show that the model estimating total capacity reduction had a better fit. Three parameters ( incident category, total number of lanes and number of lanes affected) were found to be statistically significant at the 95% confidence interval in estimating total capacity reduction. Capacity reduction is higher for incidents occurring during congestion than for incidents occurring before congestion or downstream of the road section, and increases with the number of lanes and the number of lanes affected. There is no linear relationship found between incident capacity / capacity reduction and number of lanes affected. T his dissertation considered capaci ty for shoulder plus one lane or two lanes affected conditions, however the number of data points w as not adequate for those to be included in the model development. Thus it is recommended that additional data be collected for those types of incidents. With respect to incident data collection, ideally incidents should be reported such that the number of lanes closed throughout the incident is reported. The Portland, Oregon database provides such an incident log, which greatly facilitates the modeling of incident capacity.

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127 Table 51 Capacity e stimates for non incident conditions (Units: veh/h/ln) Location # L anes Section l ength (mi) # Data points (days) Range Average (S.D.)* Breakdown f low ( r ange) Maximum p re breakdow n f low Av g f low for 10 m in b efore b reakdow n Av g. d ischarge f low Breakdow n f low Maximum p re breakdow n f low Av g f low for 10 m in b efore b reakdow n Avg d ischarg e f low Minneapolis MN 2 3 35 13502370 1920 2610 1614 2271 1435 1896 1876 (218)* 2181 (163)* 1879 (129)* 1644 (96)* Portland, OR 2 7 32 15302565 1935 2565 1296 2118 1414 2025 2010 (246)* 2238 (161)* 1858 (151)* 1741 (146)* Weighted a verage 1940 (232)* 2208 (162)* 1869 (140)* 1690 (120)* Toronto, Canada 3 6.5 56 14202520 1840 2560 1512 2264 1580 2046 2090 (247)* 2330 (162)* 2041 (170)* 1865 (124)* Sacramento, CA 3 10.4 35 14402280 1860 2460 1597 2154 1183 1843 1943 (199)* 2174 (107)* 1901 (97)* 1563 (142)* Weighted a verage 2033 (229)* 2270 (141)* 1987 (142)* 1749 (131)* Sacramento, CA 4 10.4 40 630 2100 1680 2265 948 1962 1100 1756 1750 (256)* 2018 (108)* 1783 (176)* 1567 (115)* San Diego, CA 4 2.4 39 13052175 1860 2310 1611 1979 1422 1890 1868 (160)* 2075 (113)* 1829 (86)* 1665 (85)* Weighted a verage 1808 (209)* 2046 (110)* 1806 (131)* 1615 (100)* San Diego, CA 5 2.4 34 13922076 1812 2076 1660 1866 1473 1741 1774 (160)* 1928 (70)* 1756 (58)* 1635 (66)* Numbers in the parentheses indicate the standard deviations (S.D.) of the flow parameters.

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128 T able 5 2 I ncident c apacity and n umber of l anes affected # Lanes open # Lanes affected # Data points (days) Av g. flow per total lanes (veh/h/ln) Av g. flow per open lanes (veh/h/open lane) Minimum 10 min flow rate (veh/h/ln) Avg. S.D. Avg. S.D. Avg. S.D. 0 2 11 418 118 836* 237 237 177 shoulder +2 6 763 392 1289* 785 410 284 1 1 28 1004 321 2031 627 858 316 shoulder +1 2 798 363 1595 725 443 494 2 8 756 268 2267 803 541 295 2 Shoulder 14 1383 292 1383 292 1268 295 1 28 1390 275 1390 413 792 308 3 0 1 1388 n/a 1388 n/a 1180 n/a Note: *assumes there is a passage for the vehicles on the shoulder or between the lanes, or that all lanes are closed only for a brief amount of time. T able 5 3 Comparison of incident capacity at d ifferent sites # Lanes open Minnesota site Portland site Toronto site # Data Avg. S.D. # Data Avg. S.D. # Data Avg. S.D. Av g discharge flow during incident & congestion (veh/h/open lane) 0 2 1043* 216 15 989* 560 n/a n/a n/a 1 6 1592 487 25 2070 629 7 2387 786 2 13 1428 264 8 1275 214 23 1399 457 3 n/a n/a n/a n/a n/a n/a 1 1388 n/a Minimum 10 min flow rate (veh/h/ln) 0 2 305 159 15 297 240 n/a n/a n/a 1 6 622 309 25 856 348 7 589 283 2 13 1309 260 8 765 95 23 795 344 3 n/a n/a n/a n/a n/a n/a 1 1180 n/a Note: *assumes there is one pass for the vehicles on the shoulder or between the lanes.

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129 T able 54 Comparison of p ercent of f reeway capacity a vailable under i ncident conditions Author Number of lanes Lanes blocked shoulder 1 lane 2 lanes 3 lanes Goolsby 1971 3 (27 data points) 0.67 0.50 0.21 0.00 HCM 20 1 0 2 0.81 0.35 0.00 N/A 3 0.83 0.49 0.17 0.00 4 0.85 0.58 0.25 0.13 5 0.87 0.65 0.40 0.20 Smith et al., 2003 3 (27 data points) N/A 0.37 0.23 N/A Chin et al., 2004 2 0.75 0.32 0.00 N/A 3 0.84 0.53 0.22 0.00 4 0.89 0.56 0.34 0.15* 5 0.93* 0.75 0.50 0.20* Lu and Elefteriadou, 201 1 (average discharge flow) Lanes affected 2 (60 data points) 0.77 0.50 0.14 N/A 3 (30 data points) N/A 0.43 0.32 N/A Lu and Elefteriadou, 201 1 (av g flow 10min before breakdown) 2 (60 data points) 0.68 0.46 0.13 N/A 3 (30 data points) N/A 0.40 0.29 N/A Note: assumed.

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130 T able 5 5 Effects of various factors on parameters of incident capacity Note: Incident location B bottleneck, NB nonbottleneck. Incident category 1incidents occurring during congestion, 0 incidents before congestion or downstream. T able 5 6 Estimates of p arameter s for regression to e stimate the minimum 10min flow rate ( veh/h/ln) Parameter Description Estimate Error t Value Pr>|t| i nccat In cident category: 1 during congestion 165.8 67.9 2.44 0.0166 n laneaff 1 One lane affected 885.5 46.2 19.17 <.0001 n laneaff 2 Two lanes affected 408.5 69.6 5.87 <.0001 n laneaff shoulder Shoulder affected 1291.2 79.0 16.35 <.0001 R square 0. 49 Root MSE 29 3 20 Factors Incident category Incident location Total # lanes Speed limit (mph) 1 0 B NB 2 3 55 60 Total Number of data point (days) 31 69 49 51 61 39 48 51 Av g discharge flow during inci. & cong. (Veh/h/open lane) 1481 1616 1632 1519 1572 1578 1604 1551 Minimum 10 min flow rate (veh/h/ln) 658 819 728 809 785 744 666 864 0 lane open Number of data point (days) 6 11 11 6 17 0 15 2 Av g discharge flow during inci. & cong. (Veh/h/open lane) 978 1005 1077 845 996 N/A 989 1043 Minimum 10 min flow rate ( veh/h/ln) 299 297 353 198 298 N/A 297 305 1 lane open Number of data point (days) 13 25 23 15 29 9 25 13 Av g discharge flow during inci. & cong. (Veh/h/open lane) 1890 2145 2068 2043 2004 2232 2077 2021 Minimum 10 min flow rate (veh/h/ln) 694 809 810 708 841 540 856 604 2 lane open Number of data point (days) 12 32 14 30 15 29 8 36 Av g discharge flow during inci. & cong. (Veh/h/open lane) 1290 1419 1369 1392 1390 1382 1275 1409 Minimum 10 min flow rate (veh/h/ln) 799 995 856 982 1231 805 765 986

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131 T able 5 7 Estimates of p arameter s for regression to e stimate the total capacity r eduction ( veh/h) Parameter Description Estimate Error t value Pr>|t| i nccat Incident category: 1 during congestion 386.5 167.4 2.31 0.0234 n lane T otal number of lanes 1361.1 166.6 8.17 <.0001 n laneaff 1 One lane affected 1171.6 442.7 2.65 0.0097 n laneaff 2 Two lanes affected 76.7 442.6 0.17 0.8629 nlaneaff shoulder Shoulder affected 2008.3 387.7 5.18 <.0001 R square 0.6 7 Root MSE 718.4 0

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132 Figure 51. Capacity parameters by number of lanes

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133 CHAPTER 6 AN INVESTIGATION OF THE PROBABILITY OF BREAKDOWN AND INCIDENT INDUCED BREAKDOWN AT FREEWAYS Previous research has investigated the occurrence of flow breakdown on freeways, which is defined as the beginning of congestion. It represents the transition from relatively free followin g traffic to congestion, or stop and go traffic There are several models reported in the literature that predict the occurrence of breakdown (Elefteriadou et al., 1995, Evans et al., 2001, Brilon et al., 2005). Generally, these models predict breakdown due to demand (demandinduced breakdown) as a function of flow: the higher the freeway and ramp flows, the higher the probability of breakdown. One of the most popular methods used to develop breakdown models is the Product Limit Method (PLM) that is based on the work by Brilon et al (2005). The method is also called the KaplanMeier (1958) method. This method uses lifetime data analysis for estimating the time until failure of mechanical parts or the duration of human life. Generally, the probability of fail ure increases with time, which is true in the relationship between breakdown occurrence and flow. Even though this method has been used to describe the probability of demandinduced breakdown, there is limited research on the phenomenon of freeway breakdow n induced by incidents ( incident induced breakdown). The same methods may be used to examine the relationship between incident induced breakdown and flow. This is because the mechanisms of demandinduced breakdown and incident induced breakdown have certai n similarities. Microscopic level driver behaviors, such as car following and lane changing, can lead to flow breakdown, and can also lead to incidents. Therefore, it is possible that methods that predict demandinduced

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134 breakdown can also be used in predic ting the probability of incident induced breakdown. The objective of the chapter is to apply the product limit method to estimate the occurrence of breakdown under both non incident conditions and incident conditions, and to compare the models developed f or different conditions and different sites. Several different models are developed based on various traffic flow parameters (flow, occupancy, difference between speed limit and operating speed, standard deviation of speed, and average variation of speed) and the results are compared to determine which parameters are most useful. The types of models developed in this chapter could ultimately be used in formulating and applying real time advanced traffic management systems and various freeway management strategies. Overview of the Product Limit Method ( PLM ) The PLM is based on the work by Kaplan and Meier (1958), which uses lifetime data analysis for estimating the time until failure of mechanical parts or the duration of human life. It takes advantage of the fact that the N year survival rate is equal to the product of all of the survival rates of the individual intervals leading up to time N. The lifetime distribution function is given by: ( ) = 1 ( ) ( Eq. 6 1) Where, t T P t F ) ( is the distribution function of a lifetime, T is lifetime duration ( ) = ( > ) is the survival function The product limit estimator of the survival function is given by:

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135 j j j t tn n t Sj ( Eq. 6 2) Where, is the number of items with lifetime is the number of failures or deaths at time In the context of freeway breakdown, the event of a failure at time t is the event of a breakdown at volume q, and the lifetime is the maximum prebreakdown volume. Thus, equation 6 1 can be modified to calculate the distribution of breakdown probability, as shown in the following relationship: ( ) = ( ) = 1 ( > ) ( Eq. 6 3) Where, ( ) is breakdown probability distribution is the observed traffic volume (veh/h/ln) is the traffi c volume in interval i which is the one prior to the drop in speeds, defined as the breakdown flow (veh/h/ln) ( > ) is the probability that the breakdown volume is greater than the observed volume (i.e., the probability that no breakdown will occur up to that volume) Equation 6 2 can then be written as follows : B i k d k q S q q pi i i q q i ii ) ( : ( Eq. 6 4) Where, is the observed traffic volume (veh/h/ln) is the traffic volume in interval i, which is the one prior to the drop in speeds, defined as the breakdown flow (veh/h/ln)

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136 is the number of intervals with a traffic volume of is the number of breakdowns at a volume of { } is the set of breakdown intervals The corresponding breakdown probability function is : B i k d k q Fi i i q q ii 1: ( Eq. 6 5) If each observed volume that causes breakdown is considered s eparately (that is, only one observation of breakdown for every maximum prebreakdown volume, = 1 ), then equation 65 becomes: B i k k q Fi i q q ii 1 1: ( Eq. 6 6) In applying the PLM, 1 minute time intervals are used to identify flow breakdown. Brilon et al ( 2005) pointed out that only rather short observation intervals (ideally one minute or even less ) are useful for analysis, otherwise the causal relationship between traffi c volume and breakdown would be too weak. A total of 10 minute interval s before the demandinduced breakdown are used : the last 1 min is used to represent breakdown flow in the equations and the others are nonbreakdown flows This determination is based on the work of Elefteriadou et al. ( 200 9). D ata analysis showed that flow rates much earlier than the breakdown do not contribute to the calculation results. As mentioned earlier, the mechanisms of breakdown and incidents have certain similarities and thus the methods that predict the probability of for demandinduced breakdown could also be used in predicting the probability of incident induced breakdown.

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137 Application of the Product Limit Method for Incident Conditions In order to apply the PLM to model incident induced breakdown, the equations and respective parameters are translated to consider parameters related to incident s, rather than those related to breakdown. The incident induced breakdown interval is the one immediately preceding an incident whic h has led to congestion. Several models are developed based on several different traffic parameters. Flow and occupancy which have been used to predict the probability of breakdown, are used, for comparison purposes. Models are also developed based on other parameters that might be related to breakdown occurrence: speed difference (speed limit minus speed), 5 min standard deviation of speed, and 5min average variation of speed (CVS). Based on the above, equation 6 3 becomes : ( ) = ( ) = 1 ( > ) ( Eq. 6 7) Where, ( ) is the i ncident induced breakdown probability distribution ( > ) is the probability that the incident induced breakdown volume is greater than the observed volume (i.e., the probability that no incident induced breakdown will occur up to that volume). According to the PLM it is given by : B i k inc k q q Pi i i q q i incinci : ( Eq. 6 8) The corresponding incident induced breakdown probability function is given by: B i k inc k q Fi i i q q i incinci 1: ( Eq. 6 9) Where,

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138 q is the observed traffic volume (veh/h/ln) is traffic volume in interval i, which is the one prior to the incident induced breakdown (veh/h/ln) is the number of intervals with a traffic volume of is the number of incident induced breakdowns at a volume of { } is the set of incident induced breakdown intervals (1minute observations) { } is the set of intervals prior to the incident induced breakdown If each observed volume that causes an incident is considered separately (that is, only one observation of incident induced breakdown for every maximum preincident volume, inc = 1 ), then equation 69 becomes: B i k k q Fi i q q i incinci 1 1: ( Eq. 6 10) Similarly to the analysis for demand induced breakdown, 1minute time interval s are used in the analysis, and data for 10 minutes before the incident induced breakdown were used. The next three sections present the use of the product limit method to estimate the occurrence of breakdown both due to demand and due to incidents, and makes the comparisons. Probability of D emand induced B reakdown This section first presents the data us ed and describes in some detail the estimation of the probability of demandinduced breakdown. It then presents the results based on the five traffic parameters identified in the previous section and based on these results recommends the parameter that is most appropriate to estimate the probability of demandinduced breakdown.

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139 Description of D ata and A nalysis P rocedure Data collected from three sites are used in this chapter: Toronto, Minneapolis, and Portland, as they have more incidents verified. Table 6 1 provides an overview of the study site characteristics for the sites used in this chapter and the data period. Data during nonincident conditions (with no incident) were analyzed at the following bottleneck locations: two bottlenecks at the Toronto si te, one bottleneck at the Minneapolis site, and four bottlenecks at the Portland site (two locations during the AM period and two locations during the PM period). At the Toronto site, only data at the main bottleneck 510 DES (which has much more breakdown data points than the other bottleneck) are used in developing the demandinduced breakdown models. These data are used in developing a probabilistic model of demandinduced breakdown, based on each of the five traffic parameters. Models for each site and f or all the data are developed. The following steps are followed: (1) For each demandinduced breakdown occurrence, obtain the average 1minute parameter for 10 minutes prior to the breakdown. The parameters 5minute standard deviation of speed (5min std.v) and 5 minute average variation of speed (5 min cvs) are calculated for each interval based on the speeds during the previous 5 minutes. Thus, speeds from the 15 minutes prior to the breakdown are used in calculating these two parameters. Use the parameter of the last minute as the breakdown interval and the other values as the non breakdown intervals (2) Calculate the breakdown probability using equations 6 3 through 6 6 (3) D evelop the probability distribution curve as a function of the subject parameter. Demand induced B reakdown M odels Flow based model Flow has been the parameter mostly used in developing such models in previous research. The results for the set of data used in this chapter are shown in Figure 6 1. The horizontal axis shows the flow rate, while the vertical axis indicates the probability

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140 of demandinduced breakdown. The figure shows that the probability of demandinduced breakdown is very small for flows less than 1,600 veh/h/ln, and increases to about 40% when the flow reaches 2,500 veh/h/ ln. When flow rate exceeds 2,500 veh/h/ln, the probability of demandinduced breakdown increases greatly. As shown in Figure 6 1, t he probability curves at the three sites do not differ much when flow is low (below 2,100 veh/h/ln) The probability values are in the range of 5% to 11% at the three sites for flow rates around 2,000 veh/h/ln. However, the differences in probabilities at the three sites increase when flow increases (mostly when it exceeds 2,200 veh/h/ln). More specifically, the Toronto site has a lower probability of demandinduced breakdown than the other two sites at the same flow value. For example, at a flow rate 2,220 veh/h/ln, the probability is about 12% at the Toronto site and about 27%, and 23% at the Minneapolis and Portland sites, respectively. This indicates that breakdown is triggered at a lower per lane flow rate at the other two sites than at the Toronto site. The reason might be that there are a total of three lanes at the Toronto site, while only two lanes at the Minneapolis and Portland sites (see Table 6 1). This finding is consistent with an earlier research paper, which found that threelane facilities are more productive (higher throughput per lane) than twolane or four lane facilities (Lu and Elefteriadou, 2011). Occupan cy based model Next, the probability of demandinduced breakdown is estimated based on occupancy, as shown in Figure 6 2. Figure 6 2 shows that when the occupancy is below 13%, probabilities of demandinduced breakdown are close to zero and are nearly identical at the three sites. However, there are large differences in the models for the three sites when occupancy

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141 exceeds 15%: the probability of demandinduced breakdown at the Portland site increases greatly when occupancy exceeds 15%, while at the other two sites it starts to increase significantly when the occupancy exceeds 20%. Thus, the probability of demandinduced breakdown at the Portland site is much higher than at the other two sites at the same occupancy One possible reason is that the speed l imit at the Portland site is lower (55 mph) than at the other two sites (60 mph). Thus, the same (breakdown) flow occurs at a lower speed and higher occupancy. Another, potentially related reason, is that there are comparatively more on/off ramps (especially off ramps) per mile at the Portland site than at the other two sites (see Table 6 1 ) At the Toronto site, all the 52 data points are within the main bottleneck and there is no off ramp downstream. At the Minneapolis site, only 2 of the total 34 data points have off ramps immediately downstream. However, at the Portland site, 32 of the total 33 data points represent locations with off ramps immediately downstream within 2,500 feet. Thus it is speculated that the lower speed limit, coupled with the presence of a downstream off ramp results in higher occupancies. To investigate whether the presence of downstream off ramps affected the probability of demandinduced breakdown, a comparison of probabilities of demandinduced breakdown was conducted for the two different bottleneck locations at the Toronto site. As indicated earlier, the Toronto site has two bottlenecks: one main bottleneck at detector 510 DES which has 52 nonincident data points (as shown in Figure 6 1 and Figure 6 2 ) and is free fr om downstream flow effects, and one at detector 480 DES which has 9 nonincident data points with an off ramp immediately downstream within about 2000 ft. The second set of data was not used in the previous

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142 analysis. The speed limits at the two bottlenecks are the same. The probabilities of demandinduced breakdown at the two different bottleneck locations based on flow and occupancy are shown in Figure 6 3 A ) and B ). As shown, the differences in probability of demandinduced breakdown at the two bottleneck locations are very small when estimated based on flow. However, the differences are very large when the models are based on occupancy: the probability of demandinduced breakdown at the bottleneck 480 DES, that is, the bottleneck with an off ramp immediat ely downstream, is much higher than that at the bottleneck 510 DES at the same occupancy and increases greatly when occupancy exceeds 15%. This observation is consistent with the analysis of Figure 6 2, and indicates that traffic at bottlenecks with off ramps immediately downstream would break down at a lower occupancy than at bottlenecks without off ramps immediately downstream. It also indicates that at bottlenecks with off ramps immediately downstream, breakdown occurrence is more sensitive to occupanc y than to flow, and thus occupancy might be a better indicator of breakdown for this type of design. Speed differencebased model The probability of demandinduced breakdown is estimated based on the difference between speed limit (55 mph for Portland site and 60 mph for the other two sites) and operating speed. To adjust for the differences in speed limits at different sites, the speed difference is normalized by dividing by the speed limit. The estimated probability of demandinduced breakdown is shown in Figure 6 4 The horizontal axis indicates the percent of speed lower than the speed limit, while the vertical axis shows the probability of demandinduced breakdown.

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143 As shown, the relationship for speeds above the speed limit is very similar between the three sites. For speeds lower than the speed limit however there are noticeable differences, and those increase as the operating speeds drop. The Toronto site has a low er probability of demandinduced breakdown than the other two sites. For example, at speed 16% lower than the speed limit, the probability of demandinduced breakdown is about 20% at the Toronto site and about 29% and 37 % at the Minneapolis and Portland si tes, respectively. This indicates that breakdown is triggered at a higher relative speed at the other two sites than at the Toronto site. Similar to the results based on flow, the reason for these differences could be that there are a total of three lanes at the Toronto site and two lanes at the Minneapolis and Portland site. 5 min standard deviation of speedbased model The probability of demandinduced breakdown is also estimated based on the 5 minute standard deviation of speed (5 min std.v) The probabi lity distribution is shown in Fig ure 6 5 As shown, the differences in probabilities at the three sites are very large when the standard deviation of speed exceeds approximately 6.5 Below that value, the probabilities at the Minneapolis site are lower than at the other two sites. The distribution curves do not show any clear pattern of differences between the three sites. 5 min average variation of speed based model The probability of demandinduced breakdown is estimated based on the 5 minute average variation of speed (5 min cvs) The probability distribution is shown in Fig ure 6 6 As shown, t he probability of demand induced breakdown increases with the average variation of speed.

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144 Similar to the models based on the standard deviation of speed, the differences in probabilities at the three sites are very large when the average variation of speed exceeds approximately 0.1. Below that value, the differences between the three sites are small Generally, the distribution curves do not show any clear pattern of differences between the three sites. In summary, the estimated demandinduced breakdown models seem to be different at the three sites as a function of the number of lanes: there are a total of three lanes at the Toronto site and two lanes at the Mi nneapolis and Portland sites. This is consistent with previous research which has speculated that threelane facilities are more productive in terms of per lane capacity than twolane facilities. The curves also seem to be different based on the presence o f downstream off ramps: the Portland site has comparatively more on/off ramps per mile and has off ramps immediately downstream of the breakdown locations thus demandinduced breakdown occurs at a lower occupancy at the Portland site than at the other two sites. Comparably, the flow based models are the most consistent at the three sites, but they do not show some of the differences between sites that can be seen using occupancy. The estimated models based on the 5min standard deviation of speed and average variation of speed, generally, do not show significant differences between the three sites, but they are presented here for purposes of comparison to the incident induced breakdown models. Probability of I ncident induced B reakdown This section first di scusses the process for estimating the probability of incident induced breakdown. It then presents the results based on the five traffic parameters identified above.

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145 Process for I nvestigating the P robability of I ncident induced B reakdown Only incidents that occur immediately before congestion are used in this dissertation. I ncident induced breakdown probability models are developed based on the five parameters used in developing the demandinduced breakdown models. The following steps are followed: (1) For each incident induced breakdown occurrence, obtain the average 1minute parameter for 10 minutes prior to the congestion. The parameters 5 minute standard deviation of speed (5 min std.v) and 5 minute average variation of speed (5 min cvs) a re calculated for each interval based on the speeds during the previous 5 minutes. Thus, speeds from the 15 minutes prior to the incident induced breakdown are used in calculating these two parameters. Use the parameter of the last minute before breakdown as the incident induced breakdown flow. (2) Obtain the same amount of data points with incidents that have occurred during similar time periods but have not caused congestion. (3) Calculate the incident induced breakdown probability using equations 6 7 through 6 10. (4) Develop the probability distribution curve as a function of the subject parameter. The results of the analysis are presented in the next subsection. Incident induced B reakdown M odels The resulting incident induced breakdown models are shown in Figure 6 7. As shown in Figure 6 7 A ), when using flow in developing the models, there are no major differences in the probabilities of incident induced breakdown at the three sites. When flow is below approximately 1 600 veh/h/ln, the relationship is fairly flat and the differences at the three sites are very small. I n the range of 1,600 to 2, 0 00 veh/h/ln, the slope increases and the differences between the three sites increase somewhat. For example, at flow 1,900 veh/h/ln, the probability of incident induced bre akdown is about 9 %, 15% and 8 % at the Minneapolis, Portland and Toronto sites, respectively.

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146 When flow exceeds 2, 0 00 veh/h/ln, there are few data points and the probabilities of incident induced breakdown increase greatly. The Portland site shows a higher probability of incident induced breakdown than the other two sites This may be due to the scarcity of data points at this range, as breakdown has likely already occurred due to high demand. Compared to the probability of demandinduced breakdown ( Figure 6 1), the probability of incident induced breakdown is higher at the same flow. For example, for the Portland site and for a flow of 2,000 veh/h/ln, the probability of incident induced breakdown is about 1 8 % and the probability of demandinduced breakdown is about 1 0 %. When using occupancy in developing the models ( Figure 6 7 B )), the differences among the three sites are larger: the probabilities of incident induced breakdown are the largest at the Portland site and the smallest at the Minneapolis s ite. Similarly to the differences observed in modeling demandinduced breakdown, the lower speed limit of the Portland site, coupled with the presence of a downstream off ramp likely results in increased occupancy. Compared to the probability of demandind uced breakdown (Figure 6 2), the probability of incident induced breakdown is higher at the same occupancy. For example, for the Portland site and for an occupancy of 15% the probability of incident induced breakdown is about 1 5 % and the probability of dem andinduced breakdown is about 9 %. Using the other three speed parameters in developing the models ( Figure 6 7 C ) to Figure 67 E )), the patterns are very similar to those shown for demandinduced breakdown. As the speed parameters increase, the differenc es among the three sites increase. Compared to the probability of demandinduced breakdown (Figures 6 4 to

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147 Figure 66 ), the probability of incident induced breakdown is lower at the same speed parameters. For example, for the Portland site and for a standard deviation of 6, the probability of incident induced breakdown is about 15 % and the probability of demandinduced breakdown is about 28 %. In summary, the developed probabilities of incident induced breakdown have similar shape to the probability of deman d induced breakdown based on the same parameter. Similar to the non incident conditions, the differences of incident induced breakdown probabilities among the three sites are the smallest when the model is developed based on flow. The incident induced breakdown models based on the three speed parameters have similar patterns to those for demandinduced breakdown. Comparison of D emand induced and I ncident induced B reakdown M odels This section compares t he models for demand induced breakdown and incident induced breakdown. The comparisons based on the five parameters selected are presented in Figure 6 8. Results are shown only for all sites grouped, as the comparisons at each site show very similar patterns. As shown in Figure 6 8 A ), the probabi lity of incident induced breakdown is higher than the probability of demandinduced breakdown when the flow is between approximately 1,200 and 2,200 veh/h/ln. For example, at a flow rate of 1,800 veh/h/ln, the probability of incident induced breakdown is about 8 %, and the probability of demandinduced breakdown is about 3%. Above 2,000 veh/h/ln, there are very few data points for incident conditions, and the probability of demandinduced breakdown increases much more. This indicates that for the middle range of flows, congestion is more likely to occur as a result of an incident than due to demand. Also, for incident conditions, the ranges of flow and occupancy at which congestion may result are lower

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148 than the respective range for demandinduced breakdown. For example, congestion results when flow s are in the range of 210 to 2,295 veh/h/ln for incident conditions, and in the range of 1, 35 0 to 2,565 veh/h/ln for non incident conditions The comparisons based on occupancy (Figure 6 8 B )) show similar patterns to the comparisons based on flow. However, for the other three speed parameters (Figures 6 8 C ) E )), the comparison results are quite different: the probability of demandinduced breakdown is higher than the probability of incident induced breakdown at the same speed parameter, and the differences increase with the parameters. This indicates that, f or incident conditions, speed does not drop as dramatically prior to breakdown, and speed variability is not as high as prior to a demandinduced breakdown. Conversely, high speed variability is more likely to result in a demandinduced breakdown than an incident. For example, when the 5min standard deviation is 8, there is a probability of 0.4 for a demandinduced breakdown and a probability of 0.12 for an incident induced breakdown. Another important observation is that the upper limit of these speed related parameters is higher for incident induced breakdown than the range observed for demandinduced breakdown. For example, for incidents congestion was observed to start when the 5min standard deviation of speed reached 13.7, while that upper limit for nonincident conditions is 10.5. Similar differences can be observed for the other two speed parameters. Conclusions The PLM has been used in previous research to estimate the probability of demandinduced breakdown. This chapter uses this method to estimate the probability of demandinduced breakdown, as well as incident induced breakdown and compare

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149 the two sets of models. Data collected from three freeways in North America were used in developing the models, based on five traffic parameters: flow, occupancy, the difference between speed limit and speed, 5min standard deviation of speed, and 5min average variation of speed. The following conclusions are drawn: (1) The probability of demandinduced breakdown curves as a function of flow are similar among the three sites. However the twolane sites have a higher probability of breakdown than a three lane site at the same per lane flow. This is consistent with previous research which has reported that threelane facilities are more productive in terms of per lane capacity than twolane facilities or four lane facilities. (2) The probability of demandinduced breakdown curves as a function of occupancy show some interesting differences between sites. Bottlenecks with off ramps immediately downstream were found to break down at a lower occupancy than bottlenecks without off ramps downstream. In this case breakdown occurrence is m ore sensitive to occupancy than to flow, and thus occupancy might be a better indicator of breakdown for this type of design. (3) The incident induced breakdown curves can be developed similarly to the demandinduced breakdown curves. The patterns of the curv es are similar to the demandinduced breakdown curves in that flow based curves do not show significant differences between sites, but occupancy based curves do. (4) T he distributions of demandinduced breakdown and incident induced breakdown are compared bas ed on each of the five parameters. For the middle range of flows (below 2,000 veh/h/ln), congestion is more likely to occur as a result of an incident than due to demand When flow exceeds 2,000 veh/h/ln, there are few data points with incident induced breakdown. Incident induced breakdown generally occurs at a lower range of flow and occupancy than the demandinduced breakdown. (5) For incident conditions, speed does not drop as dramatically prior to breakdown, and speed variability is not as high as prior t o a demand induced breakdown. Conversely, high speed variability is more likely to result in a demandinduced breakdown than an incident. Also, the upper limit of the speed related parameters is higher for incident induced breakdown than the range observed for demandinduced breakdown. The differences observed in the breakdown probability models between demandinduced and incident induced breakdown could potentially be used in detecting congestion and incidents and in differentiating between the two event s. As shown,

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150 there are some important differences in the range of speed, flow and occupancy at which each event occurs. Furthermore, there are differences in the probability of occurrence of each of these two events. Additional research is required however to be able to use this information in a manner that would be useful to practitioners and agencies. The types of curves developed in this chapter could also be very helpful in traffic management of freeway facilities. As shown, there are distinct patterns in the probability of breakdown of different sites, and these should be further explored to identify what design elements result in reduced probability of breakdown (both demandinduced, and incident induced). Furthermore, such curves could be developed for other sites using the method described here, and used when implementing ramp metering or Variable Speed Limit algorithms to optimize freeway operations. Potential such applications are explored in Elefteriadou et al. (2009). Finally, it is recommended to extend the PLM for predicting the occurrence of incidents, as the mechanisms of breakdown and incidents have certain similarities.

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151 Table 6 1 Summary of site characteristics and data available Site Location Length (mi) Total # of lanes Speed limit (mph) # of on/off ramps Data p eriod QEW Toronto, Canada 6.5 3 60 8 / 3 01/2005 12/2005 I 494 SB Minneapolis, MN 3 2 60 2 / 2 09/2006 08/2007 OR 217 SB Portland, OR 7 2 55 8 / 9 0107/2006 1112/2007 0112/2008

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152 Fig ure 61 Probability of demandinduced breakdown based on flow Figure 62. Probability of demandinduced breakdown based on occupancy 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 500 1000 1500 2000 2500 3000Probability Flow (veh/h/ln) All data Minneapolis Portland Toronto 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 30Probability Occ upancy (%) All data Minneapolis Portland Toronto

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153 A B Figure 63. Probability of demandinduced breakdown at the two bottleneck locations at Toronto site A) P robability based on flow B) P robability based on occupancy 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 500 1000 1500 2000 2500 3000Probability Flow (veh/h/ln) F(q)-510 DES F(q)-480 DES 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 30Probability Occupancy (%) F(q)-510 DES F(q)-480 DES

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154 Figure 64. Probability of demandinduced breakdown based on normalized speed difference Figure 65. Probability of demandinduced breakdown based on 5min std.v 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5Probability (speed limit speed)/ speed limit All data Minneapolis Portland Toronto 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 2 4 6 8 10 12Probability 5 min std.v All data Minneapolis Portland Toronto

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155 Figure 66. Probability of demandinduced breakdown based on 5min cvs 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18Probability 5 min cvs All data Minneapolis Portland Toronto

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156 A B C D E Figure 67. Probability of incident induced breakdown. A) Flow based model B) Occupancy based model C) Normalized speed differencebased model D) 5 min std.v based model and E) 5 min cvs based model 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 500 1000 1500 2000 2500 Flow (veh/h/ln) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 10 20 30 Occupancy (%) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -0.4 -0.2 0 0.2 0.4 0.6 (speed limit speed)/speed limit 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 2 4 6 8 10 12 14 5 min std. v 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.05 0.1 0.15 0.2 0.25 0.3 5 min cvs

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157 A B C D E Figure 68. Comparison of probabilities of demandinduced breakdown and incident induced breakdown. A) Flow based model, B) Occupancy based model, C) Normalized speed differencebased model, D) 5min std.v based model, and E) 5 min cvs based model. 0.0 0.2 0.4 0.6 0.8 1.0 0 1000 2000 3000 Flow (veh/h/ln) 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 30 Occupancy (%) 0.0 0.2 0.4 0.6 0.8 1.0 -0.4 -0.2 0 0.2 0.4 0.6 (speed limit speed)/speed limit 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 12 14 5 min std.v 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 5 min cvs

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158 CHAPTER 7 FREEWAY INCIDENT DET ECTION USING LIKELIHOOD OF INCIDENT FUNCTIONS In previous chapter, it is recommended to extend the Product Limit Method (PLM), which has used in developing the probability of freeway breakdown, to predict the occurrenc e of an incident, as the mechanisms of breakdown and incidents have certain similarities. The objective of this chapter is to investigate whether incident occurrence ( primarily crash es ) can be detected based on likelihood of incident functions and to comp are the results to previously developed algorithm s reported in the literature. Likelihood of incident functions are developed using the PLM for sev en different traffic parameters: average flow, standard deviation of flow, average occupancy, standard deviation of occupancy, speed difference (speed limit minus speed), standard deviation and average variation of speed. An index of incident detection is developed bas ed on these functions. This chapter also compares the results to previously developed incident detection algorithm s reported in the literature. This chapter is structured as follows. The first section presents the data set used, and defines the operational parameters that will be used in predicting the incident potential as a function of traffic states. The second s ection presents the results of the PLM for both non congested conditions and congested conditions obtains the relationship calibrated between incident potential and each traffic parameter (linear or polynomial, etc .) by regression, and proposes the incident detection index The third section evaluates the results based on detector data. The last s ection provides conclusions and recommendations.

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159 Methodology Incident occurrence is not deterministic, there is no unique combination of conditions that always lead to an incident. Traffic parameters also fluctuate significantly Thus using probabilistic techniques ( in this case the PLM) seems to be a promising approach in detecting incidents Based on literature review findings several parameters have been considered in incident detection. These include occupancy volume, speed, and standard deviation of occu p ancy This chapter also considers several other parameters that have the potential to be correlated with incidents : 5 min standard deviation of flow, speed difference (speed limit minus speed), 5min standard deviation of speed, and 5min average variation of speed. A single parameter may not correlate completely with incident occurrence, however multiple parameters used at once may provide a better indication of an incident Likelihood of incident functions are developed using the PLM technique for each parameter, and an index of incident detection is developed based on these functions The incident functions and the index are developed for noncongested and congested conditions separately, to investigate whether indices obtained by condition generate better results. This approach is d iffe rent from previous research, wherein a single incident detection algor i thm is developed for all traffic conditions or for different traffic states (e.g., McMaster). This decision is based on the observation that traffic operations under incident conditions have a similar pattern to that under recurrent congest ion It is expected that separate indices for different traffic conditions would decrease false detection of incidents during recurrent congestion.

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160 This section illustrates the methodology developed t o detect incidents, including the description of data used in the analysis, the definition of parameters that may correlate with the likelihood of an incident and the definition of traffic states, and the calculation of the PLM functions Description of D a ta Data collected from three sites are used in this chapter: Toronto, Minneapolis, and Portland, as they have more incidents verified. All crashes with durations of 5 minutes or longer are used and are classified into two groups: crashes occurring before congestion (congestion is caused by incidents), and crashes occurring during congested conditions (congestion already exists when incident occurs). Table 7 1 provides an overview of the study site characteristics for the sites used in this chapter and the respective data used in the analysis. Definition of P arameters and Traffic States Based on the discussion provided earlier, a total of seven parameters are used for incident detection: flow, 5min standard deviation of flow, occupancy, 5min standard deviation of occupancy, speed difference (speed limit minus speed), 5min standard deviation of speed, and 5min averag e variation of speed. Flow and occupancy are obtained every one minute. The standardized speed difference was developed to take into consideration the differences in the speed limits between sites. It is calculated as, = ( ) / ( Eq. 7 1 ) Where, is the speed limit at the data collection site (mph)

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161 iv is the speed at interval i (mph) Traffic operation is divided into noncongested conditions and congested conditions based on speed, because usually a drop in speed is the first indication of congestion occurrence Based on the analysis of non incident data at Toronto site, the average 1minute speed at the beginning of recurrent congestion is about 43 mi/h. Thus, a critical speed of 43 mi/h is used in dividing traffic into noncongested and congested conditions. Operation with speed higher than 43 mi/h is considered to be noncongested c onditions. For the Minneapolis and Portland sites, the average 1minute speeds at the beginning of recurrent congestion are about 40.7 mi/h and 37.4 mi/h respectively. Thus, a critical speed of 41 mi/h and 37 mi/h respectively are used in dividing traffic into noncongested and congested conditions at these two sites. The critical speed at Portland site is about 3 mph lower than that at Minneapolis site, probably because the speed limit at Portland site (55 mph) is lower than that at Minneapolis site (60 mph). Calculation of the PLM The likelihood of incident c urves are developed using the PLM for each parameter at each site for non congested and congested conditions separately. In applying the PLM the likelihood of an incident is calculated using equations 6 3 through 6 6 except that the number of breakdowns is replaced by the number of incidents. The incident interval is the one immediately preceding an incident. At each site, crashes before congestion and those during congestion are used in developing the PLM models for noncongested and congested conditions respectively. All crashes with a duration of 5min or longer except two crash es which will be used in

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162 evaluation later, are used in applying the PLM, based on each of the seven param eters illustrated above. The following steps are followed : 1) For each crash, obtain the average 1minute parameter for 10 minutes prior to the crash. Use the 10th minute parameters as the parameters that resulted in incident. 2) Obtain the same amount of data points from days without crashes during similar time periods and at the same detector locations. 3) Calculate the likelihood of an incident using equations 6 3 through 6 6. 4) Develop the likelihood distribution curve as a function of the subject parameter. Res ults of the PLM and Incident Detection Index This section presents the results of the PLM models, which predict the potential of incident occurrence, and the proposed incident detection indices for both noncongested and congested conditions. PLM for Non congested C onditions Crashes occurring before congestion are used in applying the PLM for noncongested conditions. The likelihood of incident functions are estimated based on each of the seven traffic parameter s. The results are shown in Figure 7 1 A) G). In each of the graphs the vertical axis indicates the likelihood of an incident in a oneminute interval. In these graphs, each data point represents one incident corresponding to the parameter values. It is observed from Figure 7 1 that, t he likelihood of incident has an exponential relationship with flow and occupancy, a polynomial relationship with the speed difference, and a linear relationship with the other parameters. As shown the trends are similar at the three sites, however there are some differences especially for the parameters occupancy and speed difference. For example, the likelihood of incident based on occupancy is higher at the Portland site than at the other two sites. These

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163 differences are due to reasons including different speed limits, different geometric characteristics (the number of on/off ramps downstream), and different number of lanes at the three sites. At each site, the math e matic relationship calibrated between likelihood of incident and each parameter is shown in Table 7 2 PLM for Congested C onditions Crashes occurring during congested conditions are used in applying the PLM for congested conditions. The likelihood of incident functions are estimated based on each of the seven traffic parameter s. The results are shown in Figure 7 2 A ) G ). In each of the graphs the vertical axis indicates the likelihood of an incident in a oneminute interval. In these graphs, each data point represents one incident corresponding to the parameter values. It is observed from Figure 7 2 that, for congested conditions, t he likelihood of incident has a logarithmic relationship with flow and occupancy, a polynomial relationship with the speed difference, and a linear relationship with the other parameters. These relationships are different from that under noncongested conditions, especially for flow and occupancy. Data observations show that, f or congested conditions, the likelihood of incident decrease with occupancy and flow As shown, there are also some differences in the relationships at the three sites. The reasons are similar to that for noncongested conditions. At each site, the calibrated math e matic relationship between likelihood of incident and each parameter is shown in Table 7 3 Proposed Index of Incident Detection To identify which of the seven parameters are significant in incident detection, six crashes (three occurring before congestion and three occurring during congestion) used in developing the PLM functions are selected at each site. For each crash, the likelihood

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164 of an incident based on each of the seven parameters is plotted against time. Parameters positively or negatively correlated with incident occurrence during actual incident conditions are viewed to be significant in incident detection. Conv ersely, parameters that are positively or negatively correlated with nonincident conditions are also identified. Parameters that show no clear change between incident and non incident conditions are not good indicators of incident occurrence and are thus not considered further. Two examples of the plots from Toronto site are shown in Figure 7 3 and Figure 7 4. In Figure 7 3, the incident occur s before congestion. In Figure 7 4, the in cident occur s during congestion. As shown in Figure 7 3, the blue area in the middle indicates the incident duration 15:0015:30, the two orange periods indicate the first 5min of transition states (noncongested to congested states or congested to nonco ngested states). Three parameters flow, standardized speed difference, and 5min average variation of speed, have peaks identical with the actual incident. A fourth parameter, average occupancy, has peaks contrary to the actual incident. The other three p arameters show no clear change of incident likelihood between incident and non incident conditions The similar patterns are found from Figure 7 4 and at the other two sites. Thus, the four parameters: flow, occupancy, standardized speed difference, and 5min average variation of speed, are found to be significant in incident detection. The proposed index of incident detection is calculated as the sum of the likelihood of incident based on flow, standardized speed difference, and 5min average variation of speed minus the likelihood based on occupancy.

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165 The proposed index of incident detection for Toronto site is, = 1 5 ( ) 1 0 ( )+ ( )+ ( ) The proposed index of incident detection for Minneapolis site is, = 2 0 ( ) 0 5 ( )+ ( )+ ( ) The proposed index of incident detection for Portland site is, = 1 0 ( ) 1 0 ( )+ ( )+ ( ) The coefficients before each of the parameters are obtained by trial and error. For example, when the coefficient of flow increases, the detection rate may increase and t he false alarm rate may also increase. While when it decreases, the detection rate may decrease and the false alarm rate may decrease. Although the crashes used in developing the PLM curves are all with duration of greater than 5 minutes, a crash is detect ed to occur if the index exceeds 0.5 for a continuous duration of at least two minutes. It is noted that the proposed incident detection indices for noncongested and congested conditions are in the same form. However, the PLM functions based on which they are developed are different. Model Evaluation and Comparison to Previous Research The proposed incident detection index is evaluated by detector data and compared to three previous models that are commonly used: California No. 7 California No. 8, and McMaster. A subset of data (including both crashes and nonincident days) collected from each of the three data collection sites are used to evaluate the proposed incident detection index. Information about the evaluation data at the three sites are summar ized in the first four columns in Table 7 4

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166 The evaluation data are available in two methods: raw data, which is originally recorded each 20 seconds and aggregated every one minute, and clean data, which is also aggregated every one minute and processed by a program by removing missing or erroneous observations etc ( additional information is provided in Elefteriadou et al., 2009). The proposed algorithm is used to predict the likelihood of incidents for noncongested conditions and congested conditions respectively based on both clean data and raw data. As illustrated earlier, a crash is detected to occur if the index ( total incident likelihood ) is above 0.5 for a continuous duration of at least two minutes. The evaluation results are shown in Figure 7 5 A) C) The detected incident time and duration are shown in the fifth column in Table 7 4 It is observed from Figure 7 5 that all the crashes used in evaluation are detected 1 min or 2min later than the actual crash starting time. The predicted cras h durations are also mostly the same as the actual crash durations. However, there are some intervals the index (total incident likelihood ) is above 0.5 with durations of 2 minutes or more, however, no incident is recorded to occur. These are viewed to be false alarms. The number of false alarms for each day for both clean data and raw data is summarized in the last column in Table 7 4 As shown, the clean data generates fewer false alarms than the raw data. It is also observed from Figure 7 5 that most of the false alarms occur during the AM periods, probably because there are more recurrent congestion during the AM periods. The proposed incident detection index is compared to three previous models: California No. 7, California No. 8, and McMaster algorithm based on the three measure

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167 of effectiveness: DR, FAR, MTTD. The calculation of DR and MTTD are the same as previous research. As all the incidents are detected, the DR is 100%. As shown in Table 7 4 the time differences between the incidents are detec ted and the incidents actually occur are: 1 min and 2 min at the Toronto site, 1 min and 1 min at the Minneapolis site, and both 2 min at Portland site. Thus MTTD is calculated as, = ( 1 + 2 ) /2 = 1 5 ( ) = ( 1 + 1 ) /2 = 1 0 ( ) = ( 2 + 2 ) /2 = 2 0 ( ) = ( 1 + 2 + 1 + 1 + 2 + 2 ) /6 = 1 5 ( ) FAR is calculated as the ratio of the number of false alarms to the total number of algorithm applications (executed every minute in this chapter ), which is also similar to previous research. The FAR for clean data is calculated as, = ( 3 + 0 + 0 + 0 ) /4 1 / 60 / 24 100% = 0 05% = ( 2 + 3 + 1 + 2 ) /4 1 / 60 / 19 100% = 0 18% = ( 2 + 2 + 0 + 2 ) /4 1 / 60 / 19 100% = 0 13% = ( 0 05% + 0 18% + 0 13% ) /3 = 0 12% The evaluation results of the proposed index (based on both clean data and raw data) are summarized in Table 75. As shown in Table 75, when compared to previous algorithms, the proposed index yields higher detection rate and lower mean detect time. The false alarm rates for clean data at Toronto and Portland site are lower than the California algorithms but a litter higher than the McMaster algorithms. The false alarm rates for raw data are higher than the three comparing algorithms. However, t he average FAR at the three sites is within the acceptable levels desired by operators and quite low compared to other algori thms as shown in Table 2 7 The index only needs

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168 operation data at one point, and thus is a preferable option in freeway incident detection application. Its also observed from Table 7 5 that the raw data generates the same detection rate and detection ti me as the clean data, but has higher FAR than the clean data. The average FAR based on the raw data at the three sites is still within the acceptable levels desired by operators. As indicated earlier, most of the FAR occurs during the AM periods. When appl ying the indices separately for AM and PM periods, the results are quite different. For the AM periods, the FAR are 0.1%, 0.42%, and 0.26% at the Toronto, Minneapolis and Portland site respectively, and the average MTTD is 1.4 minutes at the three sites; F or the PM periods, the FAR are 0.0%, 0.0%, and 0.04% at the Toronto, Minneapolis and Portland site respectively, and the average MTTD is 2.0 minutes. The values of DR are all 100%. This suggests that the proposed indices work much better during the PM than during the AM. Alternately, the FAR can be reduced by decreasing the coefficients before each of the parameters in the proposed incident detection index. For example, for Minneapolis site with clean data when the coefficient before flow is decreased from 2 to 1.5 and the coefficient before occupancy is decreased from 0.5 to 1.0, the index becomes (alternate index), = 1 5 ( ) 1 0 ( )+ ( )+ ( ) The resulted FAR is 0.13%, lower than the original value of 0.18%. However, one incident cannot be detected, making the DR at the Minneapolis site as 50% and the average DR at the three sites as 83.3% (= 5/6). Thus, we recommend that it is better to have higher detection rate than a very low false alarm rate.

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169 Concluding Remarks The PLM has been used in previous research to estimate the probability of breakdown. This chapter uses this method to estimate the likelihood of incident (particularly crashes) and then detect incident Data are collected from three freeways in North America. The PLM functions were first developed at each site to estimate the incident potential for both noncongested and congested conditions based on seven traffic parameters An in cident detection index is then proposed based on the PLM functions, considering parameters that correlate well with the likelihood of an incident The following conclusions are drawn: For both noncongested and congested conditions, four factors are found to be significant in incident detection. Flow, standardized speed difference, and 5min average variation of speed are positively correlated with incident s a s the likelihood of incident based on these parameters increases when an incident occurs. A fourth parameter, occupancy is negatively correlated with the likelihood of an incident. These four parameters are included in the incident detection index. The proposed incident detection index are evaluated by detector data collected from each site and compar ed to several previous algorithms. The results show that the proposed index generates higher detection rate and lower mean detect time. The c lean data generates fewer false alarms than the raw data. Most of the false alarms occur during the AM periods, pr obably because there are more recurrent congestion during the AM periods. When applying the indices separately for AM and PM periods, the results suggest that the proposed indices work much better during the PM than during the AM. The false alarm rate can be reduced by decreasing the coefficients before each of the parameters in the proposed incident detection index. However, the detection rate might also be reduced. The incident detection index proposed in this dissertation is based on data from one detec tor at a time Such an index could be very helpful in traffic management of freeway facilities T he PLM models should be developed based on data from the subject sensor, as each site generates a slightly different set of curves. Further research is

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170 needed to determine the relationship between these curves and the prevailing traffic and environmental conditions at each site. Additional validation of the proposed model would be useful to confirm that the set of indices proposed here can be applied in a wide variety of situations.

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171 Table 7 1. Overview of site characteristics and data Site Location Section l ength (mi) Total # of lanes Speed limit (mph) Data p eriod # of nonincident days # of crashes before congestion # of crashes during congestion QEW Toronto, Canada 6.5 3 60 01/2005 12/2005 55 18 (1) 9 (1) I 494 SB Minneapolis, MN 3 2 60 09/2006 08/2007 33 17 (1) 11 (1) OR 217 SB Portland, OR 7 2 55 0107/2006 3 3 (1) 1 4 (1) 1112/2007 32 0112/2008 Note: numbers in the parentheses indicate the number of data points used for evaluation. Table 72. Relationship between likelihood of incident and each parameter for noncongested conditions Parameter Toronto Minneapolis Portland Flow 0.0009*exp(0.0022*flow) 0.0004*exp(0.0028*flow) 0.0006*exp(0.0029*flow) 5 min std.flow 0.0005*std.flow 0.0636 0.0005*std.flow 0.0511 0.0005*std.flow 0.0426 Occ 0.0011*exp(0.3011*occ) 0.0007*exp(0.2803*occ) 0.0026*exp(0.2681*occ) 5 min std.occ 0.0525*std.occ 0.0576 0.044*std.occ 0.0447 0.0656*std.occ 0.0544 Speed difference 1.0039*vd^2+0.1766*vd +0.0313 0.9672*vd^2+0.4711*vd +0.0691 0.8019*vd^2+0.1742*vd +0.0274 5 min std.v 0.0241*std.v 0.0348 0.0257*std.v 0.0898 0.0247*std.v 0.0338 5 min cvs 1.0327*cvs 0.0046 1.5681*cvs 0.0762 1.0105*cvs 0.0178 Table 73. Relationship between likelihood of incident and each parameter for congested conditions Parameter Toronto Minneapolis Portland Flow 2.0453 0.27*LN(flow) 2.911 0.386*LN(flow) 2.9509 0.392*LN(flow) 5 min std.flow 0.0004*std.flow 0.0435 0.0007*std.flow 0.0711 0.001*std.flow 0.179 Occ 0.8367 0.245*LN(occ) 0.8495 0.244*LN(occ) 0.9783 0.31*LN(occ) 5 min std.occ 0.0113*std.occ 0.0109 0.0171*std.occ 0.0203 0.0147*std.occ 0.0239 Speed difference 0.4491*vd^2 0.1478*vd+0.0036 0.8296*vd^2 0.2905*vd+0.0286 0.7691*vd^2 0.3466*vd+0.0466 5 min std.v 0.0161*std.v 0.0451 0.0131*std.v 0.0324 0.0263*std.v 0.1053 5 min cvs 0.3664*cvs 0.029 0.9095*cvs 0.0944 0.8045*cvs 0.1073

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172 Table 7 4. Characteristics of evaluation data and evaluation results Site Date Incident t ime Incident type* Detected incident time # False alarms Toronto Jul 25 2005 7:147:39 During congestion 7:1 5 7:36 3 (clean), 9 (raw ) Jul 28 2005 N/A N/A N/A 0 (clean), 0 (raw ) Aug 15 2005 N/A N/A N/A 0 (clean), 0 (raw ) Aug 17 2005 18:1219:09 Before congestion 18:14 19:09 0 (clean), 0 (raw ) Minneapolis Sep 11 2006 N/A N/A N/A 2 (clean), 3 (raw) Sep 12 2006 7:568:51 During congestion 7:5 7 8: 00 & 8:26 8:45 3 (clean), 5 (raw) Sep 14 2006 N/A N/A N/A 1 (clean), 1 (raw) Oct 6 2006 11:4712:50 Before congestion 11:48 12:50 2 (clean), 2 (raw) Portland Nov 21 2007 15:3316:21 During congestion 15:35 16:2 2 2 (clean), 6 (raw) Nov 30 2007 N/A N/A N/A 2 (clean), 4 (raw) Dec 11 2007 17:1318:07 Before congestion 17:15 18:07 0 (clean), 0 (raw) Dec 12 2007 N/A N/A N/A 2 (clean), 3 (raw) Whether incident occurs before congestion or during congested conditions. Table 7 5. Comparison results of the proposed index to previous algorithm s Algorithm Site Detection Rate False Alarm Rate Mean Time to Detect (min) California No. 7 67% 0.134% 2.91 California No. 8 68% 0.177% 3.04 McMaster 68% 0.0018% 2.2 Proposed index (clean data) Toronto 100% 0.05% 1.5 Minneapolis 100% 0.18% 1.0 Portland 100% 0.13% 2.0 Average 100% 0.12% 1.5 Proposed index (raw data) Toronto 100% 0.16% 1.5 Minneapolis 100% 0.24% 1.0 Portland 100% 0.29% 2.0 Average 100% 0.23% 1.5

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173 A B C D E F G F igure 71 Likelihood of incident for noncongested conditions. A) Flow based model B) 5 min std. flow based model C) Occupancy based model D) 5 min std. occbased model E) Speed differencebased model F) 5 min std.v based model and G) 5min cvs based model 0.0 0.1 0.2 0.3 0.4 0.5 0 500 1000 1500 2000 2500 Flow (veh/h/ln) 0.0 0.1 0.2 0.3 0.4 0.5 0 100 200 300 400 5 min std.flow 0.0 0.1 0.2 0.3 0.4 0.5 0 2 4 6 8 10 12 14 16 18 20 22 Occ (%) 0.0 0.1 0.2 0.3 0.4 0.5 0 1 2 3 4 5 6 5 min std.occ 0.0 0.1 0.2 0.3 0.4 0.5 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 (speed limit speed)/speed limit 0.0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 5 min std.v 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.1 0.2 0.2 0.3 0.3 5 min cvs

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174 A B C D E F G Fig ure 72 Likelihood of incident for congested conditions. A) Flow based model B) 5 min std. flow based model C) Occupancy based model D) 5 min std. occ based model E) Speed differencebased model F) 5 min std.v based model and G) 5min cvs based model 0.0 0.1 0.2 0.3 0.4 0.5 0 500 1000 1500 2000 2500 Flow (veh/h/ln) 0.0 0.1 0.2 0.3 0.4 0.5 0 100 200 300 400 500 5 min std.flow 0.0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 20 25 30 35 40 Occ (%) 0.0 0.1 0.2 0.3 0.4 0.5 0 2 4 6 8 10 12 5 min std.occ 0.0 0.1 0.2 0.3 0.4 0.5 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (speed limit speed)/speed limit 0.0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 5 min std.v 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 5 min cvs

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175 Figure 73. Likelihood of incident potential based on each parameter for incidents occurring before congestion 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 14:10 14:20 14:30 14:40 14:50 15:00 15:10 15:20 15:30 15:40 15:50 16:00 16:10 16:20 16:30 Toronto Jan 28 2005, incident 15:0015:30 ave.flow std.flow ave.occ std.occ speed difference std.v cvs

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176 Figure 74. Likelihood of incident potential based on each parameter for incidents occurring during congestion 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 7:30 7:40 7:50 8:00 8:10 8:20 8:30 8:40 8:50 9:00 9:10 9:20 9:30 9:40 9:50 Toronto Oct 6 2005, incident 8:028:38 ave.flow std.flow ave.occ std.occ speed difference std.v cvs

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177 A -1.0 -0.5 0.0 0.5 1.0 0:00 4:00 8:00 12:00 16:00 20:00 0:00 4:00 8:00 12:00 16:00 20:00 0:00 4:00 8:00 12:00 16:00 20:00 0:00 4:00 8:00 12:00 16:00 20:00 P(inc)-predicted (clean data) P(inc)-predicted (raw data) P(inc)-actual July 25 2005 July 28 2005 Aug 17 2005 Aug 15 2005 raw data clean data Toronto Site

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178 B -1.0 -0.5 0.0 0.5 1.0 5:00 9:00 13:00 17:00 21:00 7:00 11:00 15:00 19:00 5:00 9:00 13:00 17:00 21:00 7:00 11:00 15:00 19:00 P(inc)-predicted (clean data) P(inc)-predicted (raw data) P(inc)-actual Sep 11 2006 Sep 12 2006 Oct 6 2006 Sep 14 2006 raw data clean data Minneapolis S ite

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179 C Figure 75 Evaluation results of incident detection. A) at Toronto site B) at Minneapolis site and C) at Portland site. -1.0 -0.5 0.0 0.5 1.0 5:00 9:00 13:00 17:00 21:00 7:00 11:00 15:00 19:00 5:00 9:00 13:00 17:00 21:00 7:00 11:00 15:00 19:00 P(inc)-predicted (clean data) P(inc)-predicted (raw data) P(inc)-actual Nov 21 2007 Nov 30 2007 Dec 12 2007 Dec 11 2007 clean data raw data Portland Site

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180 CHAPTER 8 FUTURE WORK This dissertation conducts analysis on the impact of incidents on freeway flow from three aspects: impact on operational conditions, impact on capacity, and impact on congestion, and detects incidents from operational conditions. In the dissertation, there are some limitations on the dataset and analysis method used. To make the findings more general and results more practical, the following areas are proposed for further research: (1) T his dissertation considered capacity for shoulder plus one lane or two lanes affected conditions, however the number of data points w as not adequate for those to be included in the model development. Thus it is recommended that additional data be collected for those types of incidents. (2) With respect to incident data collection, ideally incidents should be reported such that the number of lanes closed throughout the incident is reported. The Portland, Oregon database provides such an incident log, which greatly facilitates the modeling of incident capacity. (3) The number of lanes closed by incidents is important for incident capacity analysis For sites without information about the number of lanes affected/closed by incidents, it is suggested to predict the probability of lane closure from incident type and the number of vehicles involved in incidents. The impacts of geographic characteristics on operational conditions can be obtained by comparing the results at different sites. (4) It would be be tter to estimate the probability of incident induced breakdown and detect incidents based on the combination of several parameters. It is recommended to identify regions with high probability of incident and incident induced breakdown. (5) Further research is necessary to detect the exact location of the incident. This could be achieved by using occupancy data from both upstream and downstream stations. The location of an incident would have increasing occupancy upstream and decreasing occupancy downstream. (6) Dev elop guidelines for freeway management based on the results obtained in this dissertation. Further research on the development of ramp management strategies responsive to incidents is necessary. It is recommended to consider the capacity reduction caused by incidents, breakdown probability and incident detection in ramp metering strategy. For example, for traffic regions with high probabilities of

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181 incident and incident induced breakdown, the metering rate should be set at a lower value. It is also recommend ed to taken into consideration the location of incidents in ramp metering. For instance, when incident occurs downstream of the bottleneck, the metering rate upstream should decrease, while when incident occurs upstream of the bottleneck, the metering rate might increase. (7) The finding also can be useful in implement ing Variable Speed Limit algorithms to optimize freeway operations.

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182 APPENDIX A F ORMAT OF DATA Appendix A describes the format of data at each site. Traffic data at this site are put in comma separated text files with the format of d11_text_station_raw_ YYYY _MM_DD.txt. Each file contains information for all the detectors per day. Thus it needs to extract data for each detector from the file. The time interval is 30 seconds. The contents of the data fields are shown in Table A 1 Traffic data at this site are put in comma separated text files with the format of d 3 _text_station_raw_ YYYY _MM_DD.txt. Each file contains information for all the detectors per day. Thus it needs to extract data for each detector from the file. The time interval is 30 seconds. The contents of the data fields are shown in Table A 2 Que en Elizabeth Way ( QEW, Toronto, Canada) Traffic data at this site inc ludes mainline detector data and ramp detector data, which are comma separated text files with the format of YYYYMM DD.txt The time interval is 20 seconds. The contents of the d ata fields are shown in Table A 3. There are totally 4,322 lines in each dat a file, as the data are collected 24 hours per day. Volume, occupancy, and speed data at this site are saved in separated files, each file carries information for one detector per day. The available information concludes time and occupancy or volume or speed. The time interval is 20 seconds. The format of the data is shown in Table A 4

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183 Traffic data at this site are saved separated file, each file carries information for all the detectors per day. The available information concludes time, occupancy, speed and volume. The time interval is 1 minute. The format of the data is shown in A 5

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184 Table A 1. Format of data at I 15 SB Col. # Column / Field Units Description 1 Timestamp MM/DD/YYYY HH24:MI:SS, 2 Detector number 1108509, 3 Lane 1 Flow Veh/30 sec 14, 4 Lane 1 Occupancy % .0978, 5 6 Lane 2 Flow Veh/30 sec 11, 7 Lane 2 Occupancy % .0833, 8 . . . 23 Lane 8 Flow Veh/30 sec 24 Lane 8 Occupancy % Table A 2. Format of data at I 5 NB Col. # Column / Field Units Description 1 Timestamp MM/DD/YYYY HH24:MI:SS, 2 Detector number MM/DD/YYYY HH24:MI:SS, 3 Lane 1 Flow Veh/30 sec 314886 4 Lane 1 Occupancy % 2 5 .0978, 6 Lane 2 Flow Veh/30 sec 7 Lane 2 Occupancy % 11, 8 . . . 23 Lane 8 Flow Veh/30 sec 24 Lane 8 Occupancy % Table A 3. Format of data at the Que en Elizabeth Way ( QEW ) site Col. # Field Name Units Example field entry 1 Timestamp 2005 05 16 18:00:20 2 Total Lane Volume Veh/h 6840.018 3 Ave. Lane Occupancy % 14.3333 4 Ave. Lane Speed Km/h 90.6667

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185 Table A 4. Format of data at the US 217 SB Start time Occupancy/Volume/Speed 2006 04 03 00:00:00 07 0.5 / 90 / 51 2006 04 03 00:00:20 07 0 / 0 / 0 2006 04 03 00:00:40 07 3.5 / 360 / 42 2006 04 03 00:01:00 07 0.5 / 90 / 40 Table A 5 Format of data at the US 494 EB D2863 D2863 D2863 D2882 D2882 D2882 Occupancy Speed Volume Occupancy Speed Volume 4/2/2007 4/2/2007 4/2/2007 4/2/2007 4/2/2007 4/2/2007 12:01 AM 3.472222 29.45455 3 3.444444 21.7742 2 12:02 AM 0.361111 94.4056 1 0.555556 67.49999 1 12:03 AM 0.333333 102.2727 1 0.583333 64.28571 1

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186 LIST OF REFERENCES Abdel Aty M., Uddin Nizam, Pande A. Split Models for Predicting Multivehicle Crashes during High speed and Low speed Operating Conditions on Freeways. In Transportation Research Record 1908 TRB, National Research Council, Washington, D.C., 2005 pp .5 1 58. Agarwal M., Maze T. H. and Souleyrette R. Impacts of Weather on Urban Freeway Traffic Flow Characteristics and Facility Capacity. Proceedings of the 2005 MidContinent Transportation Research Symposium, Ames, Iowa, August 2005. Agyemang Duah, K. and Hall, F.L. Some issues regarding th e numerical value of freeway capacity, International Symposium on Highway Capacity Proceedings, Karlsruhe, Germany, 1991. pp. 1 15. Ahmed, M. S. and Cook, A. R. Application of Timeseries Analysis Techniques to Freeway Incident Detection, Transportation Research Record, No. 841, TRB, National Research Council, Washington D.C., 19 82, pp. 1921. Al Deek H., Ishak S., Khan A.A., Yarid J. Incident detection at freeway geometric bottlenecks. Department of Civil and Environment Engineering, University of Cent ral Florida. 1995. Balke, K.N. An evaluation of existing incident detection algorithms. Research Report, FHWA/TX 93/123220, Texas Transportation Institute, the Texas A&M University System, College Station, TX, November 1993. Balke K. N., Chaudhary N. A. Songchitruksa P., Chu C., Sunkari S., Nelson P., Kunchangi S., Tyagi V., Swaroop D. Dynamic Traffic Flow Modeling for Incident Detection and Short Term Congestion Prediction, Year 1 Progress Report. Report NO: FHWA/TX 06/04946 1. 2005. Banks J. H. Flo w Processes at a Freeway Bottleneck. Transportation Research Record No. 1287, Transportation Research Board, National Research Council, Washington D.C, 1990. Banks J. H. The Two Capacity Phenomenon: Some Theoretical Issues. Transportation Research Record 1320, TRB, National Research Council, Washington D.C., 1991, pp. 234241. Banks J. H. Effect of Time Gaps and Lane Flow Distributions on Freeway Bottleneck Capacity. In Transportation Research Record: Journal of the Transportation Research Board, Transpor tation Research Board of the National Academies, Washington, D.C., 2006.

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196 BIOGRAPHICAL SKETCH Cuie Lu was born in Anlu, Hubei, China. She joined in Tongji University in 2000, received her Bachelor of Engineering in t raffic e ngineering in 2004 and Master of Engineering in t raffic i nformation e ngineering & control in 2007. She was a research assistant in t ransportation e ngineering since August 2007 in University of Florida. Her research topics include traffic safety management, operational analysis, traffic modeling.