Citation |

- Permanent Link:
- https://ufdc.ufl.edu/UFE0050216/00001
## Material Information- Title:
- Pedestrian Operations in Urban Networks with Considerations of Vehicle Interactions
- Creator:
- Zheng, Yinan
- Place of Publication:
- [Gainesville, Fla.]
- Publisher:
- University of Florida
- Publication Date:
- 2016
- Language:
- english
- Physical Description:
- 1 online resource (152 p.)
## Thesis/Dissertation Information- Degree:
- Doctorate ( Ph.D.)
- Degree Grantor:
- University of Florida
- Degree Disciplines:
- Civil Engineering
Civil and Coastal Engineering - Committee Chair:
- ELEFTERIADOU,AGELIKI
- Committee Co-Chair:
- WASHBURN,SCOTT STUART
- Committee Members:
- SRINIVASAN,SIVARAMAKRISHNAN
SU,ZHIHUA STEINER,RUTH LORRAINE - Graduation Date:
- 8/6/2016
## Subjects- Subjects / Keywords:
- Crosswalks ( jstor )
Jaywalking ( jstor ) Modeling ( jstor ) Motor vehicle traffic ( jstor ) Pedestrian traffic ( jstor ) Simulations ( jstor ) Speed ( jstor ) Traffic delay ( jstor ) Traffic estimation ( jstor ) Vehicles ( jstor ) Civil and Coastal Engineering -- Dissertations, Academic -- UF pedestrians City of Gainesville ( local ) - Genre:
- Electronic Thesis or Dissertation
born-digital ( sobekcm ) Civil Engineering thesis, Ph.D.
## Notes- Abstract:
- The pedestrian mode is an important component of urban networks, and greatly affects the pedestrian facilities performance, as well as the entire network traffic operations by interacting with other traffic modes (automobile, bicycle, transit). To further advance pedestrian operational analysis in urban networks, this dissertation proposes several methods with emphasis on crossing and walking components, and provides recommendations for evaluating pedestrian facilities and guiding pedestrian route choice. For pedestrian crossings, pedestrian-vehicle interactions outside of crosswalks (jaywalking) are commonly observed especially where there are high levels of pedestrian activities. Unlike permissible crossings at crosswalks, jaywalking events are not often anticipated by drivers, which may result in less driver reaction time and different vehicle operation dynamics. This dissertation explores pedestrian jaywalking behavior and the corresponding driver reactions using field data for modeling the interactions in a micro-simulation environment. For pedestrian delay at unsignalized intersections in urban networks, this dissertation provides an improved model to mathematically estimate pedestrian delay using renewal theory with considerations of driver yielding and vehicle platooning. A generalized model is also provided to accommodate different traffic flow and driver behavior assumptions. An application with the HCM assumptions is introduced as a comparison to the HCM 2010 model. Field data and expanded simulation results both confirm the applicability and accuracy of the proposed model. For a pedestrian trip, travel route may change due to available crossing facilities, and pedestrian crossing location may affect the overall travel time. This dissertation evaluates each component along pedestrian travel path, examines pedestrian crossing choices and link delay due to vehicle interactions, and proposes pedestrian travel time estimation model as an integrated method to approximate pedestrian perspective. In summary, this dissertation analyzes pedestrian operations in urban networks with considerations of various aspects. Proposed methods for pedestrian-vehicle interactions outside of crosswalks fill the gap and offer the necessary data to create simulation models. The analytical pedestrian delay model at unsignalized intersections well accommodates urban network characteristics, and provides future expansion opportunities. The model of pedestrian travel time along travel path is an integrated approach for pedestrian operational analysis with considerations of vehicle interactions in the network. ( en )
- 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.
- Thesis:
- Thesis (Ph.D.)--University of Florida, 2016.
- Local:
- Adviser: ELEFTERIADOU,AGELIKI.
- Local:
- Co-adviser: WASHBURN,SCOTT STUART.
- Electronic Access:
- RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2017-02-28
- Statement of Responsibility:
- by Yinan Zheng.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright Yinan Zheng. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Embargo Date:
- 2/28/2017
- Classification:
- LD1780 2016 ( lcc )
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PAGE 1 PEDESTRIAN OPERATIONS IN URBAN NETWORKS WITH CONSIDERATIONS OF VEHICLE INTERACTIONS By YINAN ZHENG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FO R THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2016 PAGE 2 2016 Yinan Zheng PAGE 3 To my p arents PAGE 4 4 ACKNOWLEDGMENTS Four year study at Unive rsity of Florida provides me various valuable experiences and wonderful memories, it witnesses my growth from an undergraduate to a doctoral student who knows what to pursue for the career. I would not have been able to accomplish all the tasks without the supports of families, advisors and friends. First of all, I w ould like to thank the faculty members at University of Florida, who have taught me not only the knowledge and technical skills, but also the spirit of research and the passion of curiosity. I would like to thank my advisor, Dr. Lily Elefteriadou, for her constant support, inspiring guidance, encouragement trust and freedom in my academic and professional development. She is my role model as one of the female leaders in transportation. I would like to thank Dr. Sivaramakrishman Srinivasan for his insightfu l guidance and suggestions to my research, and Dr. Scott Washburn for being an example of outstanding professor and awesome parent. I would like to thank Dr. Ruth Steiner for her influence on a positive attitude towards life and work, and Dr. Zhihua Su for arousing my interest in data analytics. I would also like to thank them for their helpful comments from different perspectives, which are great value to my research. I am also thankful to many other professors, Dr. Yafeng Yin, Mr. William Sampson, Dr. Jam es Hobert, Dr. Kshitij Khare and Mr. Stanley Latimer, for their help during my study. I would also like to thank my parents and my boyfriend Liteng, for their selfless love and support. They shared my joys and worries they respected each of my choices, th ey accompanied me over all these years. T heir happiness is always my motivation. I am very grateful to my friends and fellow students at U niversity of Florida, who bring me fulfilment and belongings. A special thanks goes to Ines Aviles Spadoni, for her he lp and positive influence in my work and life. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 9 LIST OF FIGURES ................................ ................................ ................................ ....................... 10 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 12 ABSTRACT ................................ ................................ ................................ ................................ ... 13 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 15 1.1 Background ................................ ................................ ................................ ....................... 15 1.2 Dissertation Objectives ................................ ................................ ................................ ..... 18 1.3 Dissertation Outline ................................ ................................ ................................ .......... 19 2 LITERATURE REVIEW ................................ ................................ ................................ ....... 21 2.1 Pedestrian Crossing Behavior ................................ ................................ ........................... 21 2.1.1 Signalized Intersections ................................ ................................ .......................... 22 2.1.2 Unsignalized Intersections and Midblock Crossings ................................ ............. 22 2.1.3 Pedestrian Jaywalking Behavior (Outside of Crosswalks) ................................ ..... 24 2.2 Pedestrian Delay ................................ ................................ ................................ ............... 25 2.2.1 Signalized Intersections ................................ ................................ .......................... 26 2.2.2 Unsignalized Intersections and Mi dblock Crossings ................................ ............. 27 2.2.3 Pedestrian Jaywalking Behavior (Outside of Crosswalks) ................................ ..... 30 2.3 Pedestrian Movement ................................ ................................ ................................ ....... 30 2.3.1 Pedestrian Movement Operation Evaluation ................................ .......................... 30 2.3.2 Pedestrian Movement Modeling ................................ ................................ ............. 32 2.3.2.1 CA method ................................ ................................ ................................ ... 33 2.3.2.2 SF method ................................ ................................ ................................ .... 33 2.4 Pedestrian Travel Path ................................ ................................ ................................ ...... 34 2.5 Summary ................................ ................................ ................................ ........................... 35 2.5.1 The Need for Identifying Jaywalking Behavior (Outside of Crosswalks) ............. 35 2.5.2 The Need for Analyticall y Estimating Pedestrian Delay at Unsignalized Intersections ................................ ................................ ................................ ................. 36 2.5.3 The Need for an Integrated Approach to Estimate Pedestrian Travel Time at Travel Path ................................ ................................ ................................ ................... 36 3 MODELING PEDSTRIAN VEHICLE INTERACTIONS OUTSIDE OF CROSSWALKS ................................ ................................ ................................ ..................... 39 PAGE 6 6 3.1 Methodological Framework ................................ ................................ .............................. 39 3.1 .1 Instrumented Vehicle Study ................................ ................................ ................... 40 3.1.2 Observation Study ................................ ................................ ................................ .. 41 3.2 Data Analysis ................................ ................................ ................................ .................... 41 3.2.1 Vehicle Jaywalker Interaction Framework ................................ ............................ 42 3.2.2 Jaywalking Behaviors ................................ ................................ ............................. 42 3.2.2.1 Jaywalking locations and envi ronment characteristics ................................ 42 3.2.2.2 Jaywalking crossing speed ................................ ................................ ........... 43 3.2.2.3 Jaywalking yield recognition ................................ ................................ ........ 44 3.2.2.4 Jaywalking delay at the curb ................................ ................................ ........ 45 3.2.2.5 Summary on jaywalking behaviors ................................ .............................. 45 3.2.3 Driv er Reactions ................................ ................................ ................................ ..... 46 3.2.3.1 Driver yield rates ................................ ................................ .......................... 46 3.2.3.2 Driver decision point and distance speed relationship ................................ 48 3.2.3.3 Vehicle dynamics ................................ ................................ ......................... 49 3.2.3.4 Summary on driver reactions ................................ ................................ ....... 50 3.3 Findings and Di scussions ................................ ................................ ................................ 51 4 MODELING PEDESTRIAN DELAY AT UNSIGNALIZED INTERACTIONS IN URBAN NETWORKS ................................ ................................ ................................ ........... 69 4.1 Methodological Framework ................................ ................................ .............................. 69 4.2 Model Formulation ................................ ................................ ................................ ........... 70 4.2.1 Generalized Model ................................ ................................ ................................ 74 4.2.2 Proposed Model: Application to Urban Settings ................................ .................... 76 4.2.2.1 Vehicle safely yielding distance is less than vehicle platooned headway ( ) ................................ ................................ ................................ .......... 77 4.2.2.2 Vehicle safely yielding distance is larger than vehicle platooned headway ( ) ................................ ................................ ............................. 79 4.2.3 Application Adopting the HCM Assumptions: Comparison to th e HCM 2010 Framework ................................ ................................ ................................ ................... 80 4.3 Model Validation Using Field Data ................................ ................................ .................. 81 4.3.1 Data Collection ................................ ................................ ................................ ....... 82 4.3.2 Site Descriptions ................................ ................................ ................................ ..... 82 4.3.3 Comparison Results ................................ ................................ ................................ 83 4.4 Expanded Validation Using Simulation ................................ ................................ ........... 84 4.4.1 Comparisons between Field Data and Simulation Results ................................ ..... 85 4.4.2 Comparisons between Simulation and Proposed Model Results ........................... 85 4.5 Findings and Discussions ................................ ................................ ................................ 86 5 MODELING PEDESTRIAN TRAVEL TIME ALONG TRAVEL PATH WITH CONSIDERATIONS OF VEHICLE INTERACTIONS ................................ ..................... 100 5.1 Methodological Framework ................................ ................................ ............................ 100 5.2 Data Collection ................................ ................................ ................................ ............... 101 5.3 Crossing Del ay Estimation ................................ ................................ ............................. 102 PAGE 7 7 5.3.1 Crossing Link ................................ ................................ ................................ ....... 1 02 5.3.2 Crossing Probability ................................ ................................ ............................. 103 5.3.2.1 Variable selection ................................ ................................ ....................... 103 5.3.2.2 Model structure ................................ ................................ .......................... 103 5.3.2.3 Model specification and estimation ................................ ............................ 105 5.3.2.4 Model prediction ................................ ................................ ........................ 106 5.3.3 Crossing Delay ................................ ................................ ................................ ..... 106 5.3 Link Delay Estimation ................................ ................................ ................................ .... 106 5.3.1 Data Analysis ................................ ................................ ................................ ........ 107 5.3.2 Model Development ................................ ................................ ............................. 107 5.4 Pedestrian T ravel Time Estimation ................................ ................................ ................ 108 5.4.1 The Facts ................................ ................................ ................................ .............. 109 5.4.2 Solution ................................ ................................ ................................ ................. 109 5. 4.2.1 Link 1 ................................ ................................ ................................ ......... 109 5.4.2.2 Link 2 4 ................................ ................................ ................................ .... 110 5.4.2.3 Pedestrian Total Travel Time ................................ ................................ ..... 111 5.5 Findings and Discussions ................................ ................................ ............................... 111 6 CONCLUSIONS AND RECOMMENDATIONS ................................ ............................... 130 6.1 Pedestrian Vehicle Interaction Modeling ................................ ................................ ....... 130 6.2 Pedestrian Travel Time Estimation ................................ ................................ ................ 131 6.3 Recommendations for Future Research ................................ ................................ .......... 132 APPENDIX A THE MEAN OF PEDESTRIAN DELAY (GENERALIZED MODEL) ............................. 133 B THE PROBABILITY DENSITY FUNCTION OF THE FIRST RENEWAL (PROPOSED MODEL) ................................ ................................ ................................ ........ 135 C THE PEDESTRIAN CROSSING PROBABILITY DENSITY FUNCTION (PROPOSED MODEL) ................................ ................................ ................................ ........ 136 D THE PROBABILITY OF ACCEPTING THE FIRST VEHICLE PEDESTRIAN LAG ( ) (PROPOSED MODEL) ................................ ................................ ................................ 137 E THE PROBABILITY OF ACCEPTING THE NEXT VEHICLE PEDESTRIAN GAPS ( ) (PROPOSED MODEL) ................................ ................................ ................................ 138 F THE MEAN OF PEDESTRIAN DELAY (PROPOSED MODEL: ) ................. 139 G THE MEAN OF PEDESTRIAN DELAY (PROPOSED MODEL : ) ................ 142 H ASSUMPTIONS CHECK FOR LINK DELAY REGRESSION MODEL ......................... 143 PAGE 8 8 H.1 Outliers ................................ ................................ ................................ ................... 143 H.2 Residual Normality ................................ ................................ ................................ 143 H.3 Homogenous Variance ................................ ................................ ........................... 143 H.4 Independent Error Over Time ................................ ................................ ................. 143 H.5 Collinearity ................................ ................................ ................................ ............. 144 H.6 Linear Relationship ................................ ................................ ................................ 144 LIST OF REFERENCE S ................................ ................................ ................................ ............. 145 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 152 PAGE 9 9 LIST OF TABLES Table page 3 1 Overview of the Participan ts and Their Characteristics. ................................ ................... 65 3 2 Traffic and Environmental Variables for Each Jaywalking Location. .............................. 66 3 3 Correlation Analysis of Traffic and Environmental Variables. ................................ ......... 67 3 4 Vehicle Deceleration Rate (ft/sec 2 ) in Yielding Behaviors. ................................ .............. 68 4 1 Model Estimators ................................ ................................ ................................ .............. 95 4 2 Pedestrian Delay Comparisons (Field Data & Proposed Model). ................................ ..... 96 4 3 Pedestrian Delay Comparisons (Field Data & Proposed Mo del & Derived HCM Model & HCM 2010 Model). ................................ ................................ ............................ 97 4 4 Pedestrian Delay Comparisons (Field Data & Simulation). ................................ .............. 98 5 1 Data Collection T ime and Location. ................................ ................................ ................ 119 5 2 Selected Variables for Pedestrian Crossing Choice. ................................ ........................ 120 5 3 Model Estimation Results. ................................ ................................ ............................... 121 5 4 Sequential Model Performance. ................................ ................................ ....................... 122 5 5 Crossing Delay Estimation Methods. ................................ ................................ .............. 123 5 6 Statistical Description of Link Delay and Other Variables. ................................ ............ 124 5 7 Link Delay Model Results. ................................ ................................ .............................. 125 5 8 Link Delay Model ANOVA ................................ ................................ ............................. 126 5 9 Example Facts (Links). ................................ ................................ ................................ .... 127 5 10 Example Facts (Intersections). ................................ ................................ ........................ 128 5 11 Example Facts (Midblocks). ................................ ................................ ............................ 129 PAGE 10 10 LIST OF FIGURES Figure page 1 1 Schematic of a Pedestrian Trip in an Urban Network. ................................ ...................... 20 2 1 Schematic of Pedestrian Primary and Secondary Crossings. ................................ ............. 38 3 1 Maps of Two Study Routes for the Instrumented Vehicle Data Collection. ..................... 53 3 2 Observed Jaywalking Locations. ................................ ................................ ....................... 54 3 3 Vehicle Jaywalker Interactions Framework. ................................ ................................ ..... 55 3 4 Frequency Distributions of Pedestrian Speeds. ................................ ................................ 56 3 5 Driver Yield Rates to Jaywalkers and Permissible Crossings. ................................ ......... 57 3 6 Percentage of NY, SY, and HY Behaviors. ................................ ................................ ....... 58 3 7 Distance Speed Relationship at Driver Decision Point of HY, SY and NY For Jaywalking Events. ................................ ................................ ................................ ............ 59 3 8 Speed vs. Distance (HY, SY, NY). ................................ ................................ .................... 60 3 9 Vehicle SY Dynamics (Distance Speed Profile). ................................ .............................. 61 3 10 Vehicle HY Dynamics (Distance Speed Profile). ................................ ............................. 62 3 11 Simplified SY Reaction to Jaywalkers and Permissible Crossings. ................................ .. 63 3 12 Simplified NY Reaction to Jaywalkers and Permissible Crossings. ................................ .. 64 4 1 Schematic of the Pedestrian Delay Model Framework. ................................ ..................... 88 4 2 Pedestrian Vehi cle Interaction Scenarios. ................................ ................................ ......... 89 4 3 Comparison between the Derived HCM Model and the current HCM 2010 Model. ........ 90 4 4 Site Description s ................................ ................................ ................................ ............... 91 4 5 Density Plot and Fitted Distribution for Vehicle Headway. ................................ .............. 92 4 6 Flow Chart of Vehicle Pedestrian Inte ractions at Unsignalized Intersections ................. 93 4 7 Pedestrian Delay from Proposed Model and Simulation. ................................ .................. 94 5 1 Methodological Framework ................................ ................................ ............................. 113 PAGE 11 11 5 2 Data Collection Snapshots. ................................ ................................ .............................. 114 5 3 Schematic of Pedestrian Primary, Secondary Crossings and J ordan Curve. ................... 115 5 4 Sequential Choice Model Structure. ................................ ................................ ................ 116 5 5 Illustrations of Variables for Link Delay Estimation. ................................ ...................... 117 5 6 Numerical Example. ................................ ................................ ................................ ........ 118 PAGE 12 12 LIST OF ABBREVIATIONS ANOVA Analysis of Variance CA Cellular Automata GPS Global Positioning System HCM Highway Capacity Manual HY Hard Yield IRB Institutional Review Board LOS Level of Service MLE Maximum Likelihood Estimation MNL Multinomial Logit MUTCD Manual on Uniform Traffic Control Device NHTSA National Highway Traffic Safety Administration NY No Yield SF Social Forced STRI DE Southeastern Transportation Research, Innovation, Development and Education Center SY Soft Yield TTC Time to Conflict VJI Vehicle Jaywalker Interactions VPI Vehicle Pedestrian Interactions PAGE 13 13 Abstract of Dissertation Presented to the Graduate Sch ool of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PEDESTRIAN OPERATIONS IN URBAN NETWORKS WITH CONSIDERATIONS OF VEHICLE INTERACTIONS By Yinan Zheng August 2016 Chair: Lily Elefteriadou Major: Civil Engineering The pedestrian mode is an important component of urban networks, and greatly affects the pedestrian facilities performance as well as the entire network traffic operations by interacting with other traffic modes (au tomobile, bicycle, transit). To further advance pedestrian operational analys is in urban network s this dissertation proposes several methods with emphasis on crossing and walking components, and provide s recommendations for evaluating pedestrian facilitie s and guiding pedestrian route choice. For pedestr ian crossings pedestrian vehicle interactions outside of crosswalks (jaywalking) are commonly observed especially where there are high levels of pedestrian activities. Unlike permissible crossings at cros swalks, jaywalking events are not often anticipated by drivers, which may result in less driver reaction time and different vehicle operation dynamics. This dissertation explore s pedestrian jaywalking behavior and the corresponding driver reactions using f ield data for modeling the interactions in a micro simulation environment. For pedestrian delay at unsignalized intersections in urban networks, t his dissertation provides an improved model to mathematically estimate pedestrian delay using renewal theory with considerations of driver yielding and vehicle platooning A generalized model is also provided to accommodate different traffic flow and driver behavior assumptions. An application PAGE 14 14 with the HCM assumptions is introduced as a comparison to the HCM 2010 model F ield data and expanded simulation results both confirm the applicability and accuracy of the proposed model. For a pedestrian trip travel route may change due to available crossing facilities, and pedestrian crossing location may affect the overa ll travel time. This dissertation evaluates each component along pedestrian travel path examines pedestrian crossing choices and link delay due to vehicle interactions, and proposes pedestrian travel time estimation model as an integrated method to approx imate pedestrian perspective. In summary, t his dissertation analyze s pedestrian operations in urban networks with considerations of various aspects. Proposed methods for pedestrian vehicle interactions outside of crosswalks fill the gap and offer the nece ssary data to create simulation models. The analytical p edestrian delay model at unsignalized intersections well accommodates urban network characteristics and provides f uture expansion opportunities The model of pedestrian travel time along travel path is an integrated approach for pedestrian operational analysis with considerations of vehicle interactions in the network PAGE 15 15 CHAPTER 1 INTRODUCTION 1.1 Background The pedestrian mode is an important component of urban networks, and greatly affects the per formance of the sidewalks and crosswalks, as well as the entire network traffic operations by interacting with other traffic modes (automobile, bicycle, transit). A schematic of a pedestrian trip in an urban network is shown in Figure 1 1. The trip consist s of walking portions and crossing portions which have interactions with vehicles. Given an origin destination, pedestrians have multiple route alternatives and may encounter different traffic conditions along their path. Pedestrian trip travel time repr esents the total time a pedestrian spends from an origin to a destination within a network. There have been many studies concerning different aspects of pedestrian operations and behaviors, such as pedestrian walking speed, pedestrian delay, gap acceptance signal compliance, route choice, etc. The Highway Capacity Manual (HCM) included the pedestrian mode in the HCM 1994 (update to the HCM 1985). The most current edition (HCM 2010) provides several methodologies for evaluating the pedestrian level of serv ice (LOS) of different urban street facilities (i.e., signalized/unsignalized intersections, urban segments). The LOS score for the entire urban street facility is determined as a regression function of pedestrian LOS at intersections, at links and the roa dway crossing difficulty, which greatly depend on pedestrian delay at each location, pedestrian speed and available space respectively. However, most of the previous research do not fully cover the entire pedestrian trip and it is missing some important fi ndings in recent studies, including research on pedestrian vehicle interactions, pedestrian delay estimation, jaywalking behavior outside the crosswalks, pedestrian route choice and crossing location selection. PAGE 16 16 Pedestrian street crossing, which is commonly observed in urban networks, leads to direct interactions with motor vehicles and other road users. Different crossing locations may have different influences towards vehicular traffic and pedestrian traffic. From 2007 to 2011, an average of 12.4% of tota l crash fatalities were pedestrians ( NHTSA, 2011 ) Am ong those rashes, 73.1% occurre d at non intersections (unmarked crosswalks), while only 22.2 % were at intersections, or intersection related locations. Pedestrian crossing in locations other than marked or unmarked crosswalks ( jaywalking) is a potentially unsafe behavior. 2015) indicates that pedestrians shall not cross at any place except in a marked crosswalk between adjacent intersections at w hich traffic control signals are in operation. Vehicle jaywalker interaction (VJI) occurs where pedestrian volume is relatively high and destination attractions are randomly distributed in the vicinity of a crosswalk (for example a campus environment, a CB D of a major city). Pedestrian behaviors at unmarked crossings are reported to be quite different from crossings at marked crosswalks ( Mitman et al., 2008 ; Zhuang and Wu, 2011 ) : jaywalkers behave more cautiously (look at both directions, hurry to cross) and are more likely to cross during larger gaps. From an operations and planning perspective, it is important to understand how drivers react to jaywalkers vs. other crossing pedestrians, as well as the jaywalking gap acceptance and speeds. However t here have been few studi es analyzing the jaywalker behavior as well as examining the driver reactions to them Pedest rian delay is one of the most important performance measures for quantitatively evaluating the pedestrian vehicle interactions, as well as estimating the facility Level of Service ( HCM, 2010 ) It is highly dependent on vehicular traffic ( Adams, 1936 ; Mayne, 1954 ; Schroeder et al., 2014 ; Troutbeck, 1986 ) road geometry ( Dunn and Prett y, 1984 ; Troutbeck, 1986 ) and pedestrian behavior ( Schroeder et al., 2014 ; Schroeder and Rouphail, 2010b ; Sun et al., 2003 ) PAGE 17 17 The first pedestrian delay model for crossing at unsignalized intersections was developed by William Adams in 1936 ( Adams, 1936 ) and has been expanded/modified by various researchers ( Cowan, 1975 ; Mayn e, 1954 ; Tanner, 1951 ; Troutbeck, 1986 ; Underwood, 1961 ) The early models adopted simple ve hicle headway distributions and ignored vehicle yield behaviors. A few other researchers explored this problem by considering it as a stochastic process ( Heidemann and Wegmann, 1997 ; Weiss and Maradudin, 1 962 ) Recent pedestrian delay studies focused on calibrating and modifying the previous models for different traffic scenarios ( Guo et al., 2004 ; Schroeder and Rouphail, 2010b ; Vasconcelos et al., 2012 ) such as two stage crossing, pulsed traffic caused by signals, etc. The HCM 36) with adding the assumption of constant vehicle yield rate for estimating pedestrian delay ( HCM, 2010 ) However, those existing models may not sufficiently capture the realistic pedestrian street crossing behavior at unsignalized intersections in urban networks. Particula rly, findings from observational studies, have identified factors such as platooned traffic flow pattern ( Avineri et al., 2012 ; Bowman and Vecellio, 1994 ; Schroeder et al., 2014 ; Sisiopiku and Akin, 2003 ) driver yielding behavior ( Schroeder, 2008 ; Sun et al., 2003 ) and pedestrian yield recognition ( Schroeder et al., 2014 ; Schroeder, 2008 ) that have great importance and should be considered in the pedestrian delay model. The existing models are missing those and may no t perform well in estimating pedestrian delay in cases of high level pedestrian activities, such as in major city CBD areas, campus areas, etc. Generally, pedestrian travel time along urban segments can be a good performance measure, since it captures the pedestrian perspective and considers the time spent along the travel path including crossing at intersections, walking along the links and interacting with other road users ( Figure 1 1) Hoogendoorn and Bovy (2004) described pedestrian behavior in urban PAGE 18 18 networks as a hierarchical structure with: strategic level (departure time choice); tactical level (activity schedulin g and route choice); and operational level (road crossing and interactions). The tactical decision interacts with the operational level when, for example, pedestrian travel route may change due to available crossing facilities, and pedestrian crossing loca tion may affect the pedestrian overall travel time. This structure explains the relationship among these three levels and emphasizes the necessity for an integrated method for pedestrian operation analysis. However, most existing studies ignore these mutua l impacts or separates pedestrian walking and crossing behaviors, and pedestrian travel time is typically analyzed only at the intersection level. Thus it is necessary to link the pedestrian movement and crossing behaviors with consideration of pedestrian vehicle interactions. Travel time estimation can offer an integrated way to analyze pedestrian operations along the travel path and evaluate facility performance. In this dissertation, we identify several major issues as regards the needs for pedestrian o peration analysis in urban networks, and propose several methods specifically emphasizing pedestrian vehicle interactions outside of crosswalks, pedestrian delay estimation as well as pedestrian travel time estimation along travel path in order to approxim ate the pedestrian perspective 1.2 Dissertation Objectives The objective of this research is to propose methodologies for evaluating and analyzing pedestrian operations in urban networks with emphasis on both crossing and walking components, and to provid e recommendations for evaluating pedestrian facilities as well as guiding pedestrian route choice. Pedestrian travel time estimation at the path level is proposed as an integrated approach to approximate the pedestrian perspective in pedestrian operation a nalysis. The following tasks are performed to accomplish the above objectives: PAGE 19 19 1. Observing pedestrian jaywalking behaviors and driver reactions; modeling pedestrian vehicle interactions outside of crosswalks in urban networks; 2. Developing analytical methods to estimate pedestrian delay at unsignalized intersections in urban networks with considerations of vehicle platooned arrivals and yielding behavior; 3. Capturing the effects of pedestrian vehicle interactions on pedestrian walking time and crossing probabili ties along travel path and proposing a method to estimate the total pedestrian travel time as a quantitative measure for pedestrian operation evaluation. 1.3 Dissertation Outline The remainder of this dissertation is organized as follows Chapter 2 provide s an overview of the literature on pedestrian operation s in urban networks, including crossing behavior, pedestrian delay pedestrian movement and pedestrian travel path Chapter 3 discusses the observational studies of pedestrian vehicle interactions outs ide of pedestrian crosswalks and the methodology for quantifying and modeling their interactions in a micro simulation environment Chapter 4 provides the methodology for mathematically estimating pedestrian delay at unsignalized intersection to address dr iver yielding and platooned vehicular traffic conditions in urban networks Chapter 5 proposes an integrated model for estimating pedestrian travel time along travel path. Finally, the overall conclusions and recommendations for future work are provided in Chapter 6. PAGE 20 20 Figure 1 1 Schematic of a Pedestrian Trip in an Urban Network. PAGE 21 21 CHAPTER 2 LITERATURE REVIEW This chapter first provides a brief summary of the pedestrian crossing behavior at different locations (signalized, un signalized intersections, midblock crossing, and outside of crosswalks) with emphasis on pedestrian vehicle interactions. A review of the pedestrian delay estimation methodologies at those locations is also presented. Following that, existing pedestrian mo vement operations along with a discussion of macroscopic/microscopic modeling methods are described. Finally, methodologies for pedestrian travel path selection as well as its geometry characteristics are briefly summarized. 2.1 Pedestrian Crossing Behavi or Pedestrian crossing behaviors and the respective vehicle reactions were observed in the field and studied by a number of researchers ( Braun and Rodin, 1978 ; Coffin and Morrall, 1995 ; Guo et al., 2011 ; Li et al., 2005 ; Molin o et al., 2012 ; Ni and Li, 2012 ; Schroeder et al., 2014 ; Schroeder and Rouphail, 2010a ; Schroeder and Rouphail, 2010b ; Schroeder, 2008 ; Sun et al., 2003 ; Virkler, 1998 ) Crossing difficulty and crossing options were explored and identified as important factors for multi modal analysis ( Chu et al., 2004 ; Golledge, 1999 ; HCM, 2010 ; Holland and Hill, 2007 ; Jim Shurbutt, 2013 ; Kneidl and Borrmann, 2011 ; Mitman et al., 2008 ; Zhou et al., 2009 ; Zhuang and Wu, 2011 ) Pedestrian vehicle interactions affect pedestrian traffic operations in urban networks, as well as the pedestrian related facility performance as they may cause delay and spillback. Permissible crossi ng is defined as pedestrian crossing at marked or u nmarked crosswalks, such as at signalized intersection, unsignalized intersections and midblock crosswalks. C rossing a roadway at any point other than within a marked crosswalk or within an unmarked cross walk at PAGE 22 22 an intersection is defined as jaywalking, and jaywalkers shall yield the right of way to all vehicles upon the roadway ( 2015 ) 2.1.1 Signalized Intersections Ped estrian crossing behavior and vehicle interactions at signalized intersections depend on the traffic control features and intersection signal plans. Pedestrians may not directly interact with vehicular traffic where pedestrian volume is high and a protecte d pedestrian crossing phase is implemented. At some other intersections where right turn vehicles are allowed to turn during the red, crossing pedestrians may conflict with right turning traffic. Pedestrian signal compliance rate is another important asp ect that affects pedestrian vehicle interactions as well as pedestrian traffic operations at signalized intersections. It varies with traffic conditions, crossing treatments, signal timing designs and personal characteristics and attitudes ( Guo et al., 2011 ) The HC M (2010) indicates that pedestrian compliance is a function of the expected delay. Dunn and Pretty (1984) found that all pedestrians complied if delay was less than 10 seconds, while no pedestrians complied if the delay exceeded 30 seconds. Huang and Zegeer (2000) indicated that the overwhelming majority of pedestrians preferred the r compliance was more likely to occur at a low volume minor street approach to a signalized intersection ( Stollof et al., 2007 ) 2.1.2 Unsignalized Intersections and Midblock Crossings Pedestrians have more direct interactions with vehicles at unsignalized in tersections and midblock crossings. Generally, pedestrians are more likely to cross the street at designated facilities ( Dunn and Pretty, 1984 ; Sun et al., 2003 ) The pedestrian street crossing behavior can be regarded as a pedestrian gap acceptance problem, where the vehicle pedestrian gap is a good indicator that captures the interaction PAGE 23 23 distance between the ap proaching vehicle and waiting pedestrian. The HCM 2010 assumes pedestrians are consistent and homogeneous, i.e., all pedestrians would always seize the gap if it is greater than the critical value (which may not be completely true in reality). Other studie s have proposed distributions for critical gaps, such as log normal ( Troutbeck, 1 992 ) or random distribution ( Robertson et al., 1994 ) This probability based method considers heterogeneity in the pedestrian population and can be used to analyze pedestrian operations by pedestrian groups. But these models ignore the pedestrian vehicle interactions that influence the variability of critica l gaps. Recent studies conducted field observations and indicated that pedestrian characteristics (age, assertiveness, volume, location), traffic characteristics (platoon, gap size), vehicle characteristics (speed and distance), geometry characteristics (c rossing treatments) all influence the pedestrian gap acceptance as well as the pedestrian operations at unsignalized intersections or midblock crossings ( Avineri et al., 2012 ; Schroeder and Rouphail, 2010a ; Schroeder, 2008 ; Sun et al., 2003 ; Wang et al., 2010 ) However, there exist other factors in pedestrian vehicle interactions that have not been considered, such as the maximum pedestrian wait time, vehicle wait time, etc. Driver yield behavior has been commonly o bserved when interacting with street crossing pedestrians and may significantly affect the interactions as well as pedestrian operations at unsignalized intersections /midblock crossings ( Salamati et al., 2013 ; Schroeder et al., 2014 ; Schroeder, 2008 ; Sun et al. 2003 ) The yield rate varies under different conditions. For example, it was found that the drivers were more likely to yield with low vehicle travelling speed ( Salamati et al., 2011 ; Schroeder and Rouphail, 2010a ) travelling in a platoon ( Schroeder et al., 2014 ) to more assertive pedestrians ( Schroeder and Rouphail, 2010a ) and within an environment with higher pedestrian activities ( Schroeder and Rouphail, 2010b ; Zheng et al., 2015a ) The PAGE 24 24 behavior of the vehicle in front might also have an impact on the following vehicles ( Schroeder and Rouphail, 2010a ; Schroeder, 2008 ) Findings from pedestrian crossing behavior studies can provide the assumptions for developing pedestrian delay models. Previous research has found that pedestrians are more likely to cross the street at designated facilities ( Dunn and Pretty, 1984 ; Sisiopiku and Akin, 2003 ; Sun et al., 2003 ; Zheng et al., 2015a ) and the average crossing speed was found to be 4 ft/sec for the general population ( HCM, 2010 ) The pedestrian crossing decision has been found to be hi ghly dependent on the distance, as well as the driver yielding decision and the vehicle speed ( Dunn and Pretty, 1984 ; Schroeder et al., 2014 ; Schroeder, 2008 ; Sun et al., 2003 ; Zheng et al., 2015a ) However, no st udies have focused on the analysis of vehicle operation dynamics nor the speed behavior towards the crossing pedestrians. 2.1.3 Pedestrian Jaywalking Behavior (Outside of Crosswalks) Pedestrian crossing outside of a marked or unmarked crosswalk (i.e. jaywa lking), is one of those pedestrian behaviors that affect safety and operations. Pedestrian jaywalking behavior is commonly observed in the field, especially within an environment with high levels of pedestrian activities ( Zheng et al., 2015b ) Unlike permissible crossings at crosswalks, jaywalking events are not of ten anticipated by drivers, which may result in lower driver reaction time, different vehicle dynamics, as well as different pedestrian operations ( Zheng et al., 201 5a ; Zheng et al., 2015b ) Pedestrian jaywalking behavior may highly affect the pedestrian route selection as well as the pedestrian trip travel time. To date, limited quantitative and behavioral research has been conducted to investigate this interaction or simulate it microscopically. A ccording to Golledge (1999) and Kneidl and Borrmann (2011) pedestrians prefer to walk long and straight routes to a destination in an urban environment (SALL algorithm). Mitman et al. (2008) compared pedestrian behaviors at marked and unmarked crosswalks and indicated that pedestrians at unmarked crosswalks are more likely to look at both ways before PAGE 25 25 crossing, to run, and to wait for larger gaps. Zhuang and Wu (2011) found that jaywalkers in the urban cities of China are less likely to have a crash when they are m iddle age d are in larger crossing groups, are more attentive to traffic The highway environment impacts on crossing behaviors or preferences have been examined by several papers. Chu et al. (2004) modeled the role of street environment in the way people cross urban roads. Crossing distance and traffic volume were found to highly affect why people cross where they do ( Jim Shurbutt, 2013 ) A study conducted by the Federal Highway Admini stration (FHWA) indicated that the environmental factors that ultimately influence pedestrian jaywalking locations were: the distance between marked crosswalks, annual average daily traffic (AADT), physical barriers that might prevent pedestrians from easi ly crossing the roadway, the presence and location of bus stops, the number of potential pedestrian trip originators and destinations, the presence of a and the presence of a T intersect ion between the two marked crossings ( Jim Shurbutt, 2013 ) S everal studies applied the Theory of Planned Behavior crossing, and provided ( Evans and Norman, 2003 ; Holland and Hill, 2007 ; Zhou et al., 2009 ) It was found that erceived behavior control was one important factor on crossing intentions, and it was highly affected by the crossing facilities and environment. Also, pedestrians were aware of the risk of illegal crossing, but sometimes they still chose to jaywalk. 2.2 P edestrian Delay Pedestrian delay is often used as a key performance measure for quantitatively evaluating the pedestrian vehicle interactions, as well as estimating the facility Level of Service ( HCM, 2010 ) It is highly dependent on vehicular traffic ( Adams, 1936 ; Mayne, 1954 ; Schroeder et al., PAGE 26 26 2014 ; Troutbeck, 1986 ) road geometry ( Dunn and Pretty, 1984 ; Troutbeck, 1986 ) and pedestrian behavior ( Schroeder et al., 2014 ; Schroeder and Rouphail, 2010b ; Sun et al., 2003 ) 2.2.1 Signalized Intersections Pedestrian delay is defined as the wait time due to signal effects and conflicts wit h turning vehicles or pedestrians at crosswalks. The HCM (2010) only considers signal effects, and it assumes random pedestrian arrival rate, fixed pedestrian timing, no pedestrian conflicts, and 100% pedestrian compliance. The delay model used in the HCM 2010 is as follo ws: (2 1) where is cycle length (s); i s effective walk time (s), depending on crossing treatment type. This model is a theoretical function of cycle length and pedestr ian phase duration. It is not applicable for pedestrian crossing in groups such as two stage crossings or under high pedestrian volume condition. A New York City study ( Bloomberg and Burden, 2006 ) indicated that 3 seconds as a start up time was necessary to be ad ded at signalized intersections with high pedestrian volume. There are a number of studies on developing pedestrian delay model at signalized intersections. The major focuses are adjust ing the pedestrian compliance rate and pedestrian arrival pattern. Virkler (1998) added a portion of pedestrian clearance interval to actual green time in the case of pedestrian crossings during the clearance period. Braun and Rodin (1978) and Li et al. (2005) both added a parameter in their models to estimate the delay reduction due to non compliance. Li et al. (2005) found the magnitude of this parameter was affected by conflicting vehicle flow and the percentage of no complying pedestrians when there was an acceptable gap. Wang and Tian (2010) developed a delay model for signalized intersections with a median. Assuming 100% pedestrian compliance and uniform arrival rates during the first stage, PAGE 27 27 the delay model consisted of delay from the first stage crossing, delay from the second stage stage crossing beginning d uration of the first stage. Li et al. (2005) introduced another parameter in the dela y model to capture the observed pedestrian non uniform arrival pattern. The models reviewed here improved the delay accuracy relative to the HCM 2010 methods by adjusting the assumptions to be better aligned with field conditions. 2.2.2 Unsignalized Inter sections and Midblock Crossings The first pedestrian delay model at unsignalized intersections was proposed by Adams in 1936 in one of the earliest theoretical traffic papers ( Adams, 1936 ) The g ap acceptance meth od was applied and he assumed that vehicles and pedestrians arrive randomly, and both behave consistently. The pedestrian will accept the gap if and only if the vehicle pedestrian gap is larger than the critical gap; otherwise, he/she will stay and wait fo r another acceptable gap. Tanner (1951) street crossings. He also assumed random arrival of vehicles and pedestrians, but he further considered non uniform critical gaps for different pedestrians and considered the distribution of pedestrian group size (in the case of pedestrian crossing in groups). Most of the early models are called M1 models, since they all shared a common assumption: the vehicle arrival s follow t he Poisson distribution (vehicle headway s are distributed as negative exponential). As noted in other studies ( Troutbeck and Brilon, 1997 ) the Poisson distribution predicts too small hea dways The s hifted exponential distribution was proposed instead, which assumed a minimum headway (M2 model), to overc o me that drawback. However, this approach vehicles travelling in a group (platoon). In 1975, Cowan developed the M3 model which PAGE 28 28 ( Cowan, 1975 ) The platoon size was assumed to follow the geometric distribution. This model offered a realistic arrival assumption for stochastic modeling. Troutbeck (1986) estimated the average delay at an unsignalized intersection with two major streams based on the M3 model and indicated that the platoon size did h ave a major impact on average delay and degree of saturation of the minor stream (pedestrian departure). Akcelik and Chun g (1994) compared the M1, M2 and M3 models with field data from single lane traffic and simulation data from multi lane traffic. They recommended the M3 model for general use in traffic modeling. Mayne (1954) generalized ( 1951 ) and considered a ge neral distribution for vehicle headways. Guo et al. (2004) proposed a pedestrian delay model with pulsed traffic flow caus ed by traffic signals. He assumed that each arriving pedestrian will face one of the following possible scenarios: a bunched flow with no suitable gap to cross, a flow where vehicles travel randomly (there may be gaps to cross), and a clearance time (large r than the pedestrian critical gap) where all the waiting pedestrians can cross. The model was based on pre timed isolated signals with the bunched flow starting at the beginning of the equivalent green time and the clearance time equivalent to signal lost time. We did not find any analytical models in the literature that consider driver yielding possibilities (i.e., they assumed the pedestrians only cross in gaps) which may significantly affect the pedestrian delay. The HCM 2010 provides a method to estima te pedestrian delay for major street crossing s at two way stop controlled intersections ( HCM, 2010 ) It assume s random pedestrian arrivals, random vehicle arrivals and equal distribution of traffic volume on all through lanes of both directions. The p edestrian delay is divi ded in two parts: gap delay (when pedestrians cross during an available gap) and yield delay (when pedestrians cross during a vehicle yield). The average PAGE 29 29 delay is thus c alculated as the sum of the products of each delay with the corresponding probability estimation, while assuming independent vehicle yielding and constant yield rate for the yield delay estimation ( HCM, 2010 ) There are some studies using renewal theory to address the pedestrian delay pro blems at two way stop controlled intersections ( Heidemann and Wegmann, 1997 ; Weiss and Maradudin, 1962 ) single lane roundabouts ( Flannery et al., 2005 ) Renewal theory is a branch of probability theory that generalizes stochastic proces ses. The mean and variance of the queueing delay can be estimated from the models. However, some of the studies were validated to perform well only under certain conditions. For example, the model by Flannery et al. (2005) was validated to perform well only under moderate cir culating steam flow rates. Weiss and Maradudin (1962) assumed vehicle arrivals along the major street are uncorrelated, with a known probability distribution function, and the pedestrian crossing probability (gap acceptance) is a known function. Based on renewal t heory, a general form of pedestrian delay distribution was developed as a convolution integral equation, and the moments were found by Laplace transformation. Their results could be further expanded to address other problems in traffic delay, such as impat ient pedestrians whose gap acceptance depends on the passage of major street vehicles, correlated vehicle gaps by using the theory of semi Markov process, etc. Driver yielding behavior was not covered in this study. Heidemann and Wegmann (1997) applied the M/G2/1 queuing model and generalized several mathematical results for queuing problems at unsignalized intersections, such as queue length, delay, capacity, etc. This model also applied renewal theory for analyzing the queuing PAGE 30 30 system at unsignalized intersections, but the inter arrival distribution was required to be negative exponential. 2.2.3 Pedestrian Jaywalking Behavior (Outside of Crosswalks) been done. 2.3 Pedestrian Movement Pedestrian walking speed and available space are the major elements of pedestrian movem ent along urban segments, and are key performance measures for pedestrian movement operation evaluation. There have been many studies analyzing average pedestrian speeds under different circumstances ( Dewar, 1992 ; Fitzpatrick et al., 2007 ; MUTCD, 2009 ; Schroede r et al., 2014 ) Pedestrian movement in urban networks has been modeled by various simulation methods, including macroscopic and microscopic models, and time based or event based simulation techniques. 2.3.1 Pedestrian Movement Operation Evaluation Pede strian speed and available space are widely used performance measures for evaluating pedestrian movement in urban networks. The HCM 2010 uses the walking speed and available space along sidewalks to estimate pedestrian LOS at road links. Link LOS further d etermines the overall LOS performance of urban pedestrian facilities. For road segments, there are different estimation methods for pedestrian speed and the corresponding available space. The HCM (2010) (Chapter 17 and 23) estimates the average pedestrian speed as a function of pedestrian flow rate and effective width at urban segments (roadway and intersection) and off street facilities (walkways and stairways), as follows: (2 2) where is pedestrian flow rate p er unit width (p/ft/min); is pedestrian free flow speed (ft/s). PAGE 31 31 The HCM 2010 assumes equal demand distribution in the two directions without accounting for the impacts of unequal distributions and opposing/conflicting pedestrians. The unit width refers to the effective width, which is the total walkway width minus the width of fixed objects (trees, buildings) and shy distances (the buffer distance between pedestrians and obstacles, such as curbs). For shy distance, Stucki (2003) used 1.5 ft from walls, 1.14 ft from fences and 1 ft from small obstacles (such as street lights and trees). Hoogendo orn and Daamen (2005) used 1.5 ft for the case of pedestrian inside bottlenecks. A distance of 1.5 to 2.0 ft is used in the HCM 2010. But no reliable and robust methods to estimate shy distance have been provided in the existing studies that would be app licable in different walkway conditions ( Bloomberg and Burden, 2006 ; Hoogendoorn and Daamen, 2005 ; Pushkarev and Zupan, 1975 ) A study by the New York Department of City Planning ( Bloomberg and Burden, 2006 ) indicated that the HCM model (E quation 2 2 ) was too insensitive to changes in pedestrian volume and sidewal k width. Direction traveled, pedestrian characteristics and pedestrian density on the sidewalk should be considered as other contributing factors. For street crossing, the Traffic Engineering Handbook ( Dewar, 1992 ) suggested a speed of 3.0 to 3.25 ft/s would be more appropriate to use for signal timing. A crossing speed of 3.5 ft/s was suggested for the general population by Fitzpatrick et al. (2007) The Manual on Uniform Traffic Control Devices ( MUTCD, 2009 ) suggested 4 ft/s as pedestrian crossing speed for signal timing. The HCM (2010) uses 4.0 ft/s as uniform pedestrian crossing speed in all traffic/geometry/treatment conditions at signal intersection crosswalks. Pede strian crossing speed is affected by many factors. Some research indicates that crossing speed is a function of internal factors such as pedestrian age, and gender, as well as external factors such as pedestrian volume, grade, width, and environment ( Coffin and Morrall, 1995 ; Knoblauch et al., 1996 ) Fruin (1971) PAGE 32 32 found that the speed in both directions tended to be equal when there were no dominant flows, while in other cases, the stronger flow tended to weaken others. Blue and Adler (2000) conf irmed the impacts of cross directional pedestrian flow on speed reduction. In general, the literature indicates there is consensus about the fact that the pedestrian speed is influenced by many factors pedestrian volume, available space, age, walkway env ironment, time of day, trip purpose, etc. However, the HCM 2010 method does not consider most of them, and provides the crossing speed only at signalized intersection crosswalks. Further research at roundabouts, and all way stop controlled intersections ar e necessary. Moreover, most of the existing studies only focused on the average pedestrian speed and did not well incorporate variabilities in pedestrian behavior. 2.3.2 Pedestrian Movement Modeling Macroscopic models for pedestrian movement have been mos tly developed based on fundamental traffic flow theory and queueing theory ( Daamen et al., 2005 ; Huang et al., 20 09 ; Hughes, 2002 ; Xia et al., 2009 ) Hughes (2 002) proposed a continuum theory to understand the mechanics of pedestrian flow in large crowds. The pedestrian crowd behaved rationally and aimed to achieve the immediate goal in minimum time. Daamen et al. (2005) calibrated the fundamental traffic flow diagrams for pedestrian flow operations in congestion and provided a method to estimate the fundamental diagram from observations. Xia et al. (2009) developed a macroscopic model for pedestrian flow at a walking facility. They assumed the pedestrian chose a route based on the memory of the shortest path and tried to avoid high densities. Micro simulation of pedestrian movement behavior has been a major focus in pedestrian operations. In these, each pedestrian is considered individually. Antonini et al. (2006) tested two logit models to simulate pedestrian movement at a metro station entrance by considering pedest rian speed, direction angle and other surrounding pedestrians. Cellular Automata (CA) PAGE 33 33 models and Social Forces (SF) models are two typical approaches to simulate pedestrian movement in urban networks microscopically. 2.3.2.1 C A method CA models, which ef fectively capture collective behaviors, have been widely used for pedestrian simulation ( Davidich and K ster, 2012 ) In a CA model, the entire area of interest is covered by cells. Each cell is occupied by one pedestrian. The interactions a pedestrian may come across (e.g., nearby pedestrians, targets and obstacles) are calculated into scores. In moving to ward their destination, pedestrians would choose the neighboring cell with the lowest score. Gipps and Marksj (1985) first proposed CA modeling in pedestrian simulation. Blue and Adl er (2001) applied CA modeling and simulated several pedestrian movement behaviors, such as side stepping, conflict mitigation, and indicated that the flow patterns were consistent with well established fundamental properties. Dijkstra et al. (2001) developed a multi agent CA model of pedestrian movement as a tool to better explain how a design would influence user behaviors. Burstedde et al. (2001) developed a CA model for large systems and showed that the model allowed for faster than real time simulations. However, the CA method does not take into consideration that pedestrians may follow othe rs to cross rather than keep a certain distance with people s around and make their own decisions. 2.3.2.2 SF method SF models are commonly used for computer simulations of crowds of interacting pedestrians. Their ability to realistically describe the se lf organization of several observed collective effects of pedestrian behavior has been demonstrated ( Helbing et al., 2005 ) Helbing and Molnar (1995) developed the first SF model, which has similar principles as a Benefit Cost Cellular Model. A pedestrian is subjected to several social forces around himself/herself when moving forward to their destination, including motivation to reach their goal, and repulsive PAGE 34 34 forces of other pedestrians and of obstacles. Johansson et al. (2007) applied an evolutionary optimization algorithm for parameter specifications for an SF model. Their proposed model can be applied for large scale pedestrian simulations of evacuation scenarios and urban environments. SF models are more flexible for modeling different sizes and shapes of obstacles within the walking space, so that complicated scenarios such as evacuations during emergencies can be simulated. A comparison between SF and CA models showed that the SF model took much longer in updating pedestrian position s than the CA model, when simulating the same number of pedestrians ( Quinn et al., 2003 ) In general, for pedestrian movement models, most are developed based on traffic f low theory or basic kinematics. Given an Origin Destination pair, the pedestrian travel path is randomly selected, however, the pedestrian route choice in reality highly depends on pedestrian characteristics and traffic conditions. 2.4 Pedestrian Travel Path Pedestrian route choice is another important aspect that influences pedestrian operations. However, all the pedestrian movement simulation models mentioned in the previous sections d o mined by the result of every single simulation step of pedestrian movement. No general travel route preference or pedestrian variability were considered. Asano et al. (2010) proposed a microscopic pedestrian movement model along with a macroscopic tactical model for pedestrian route choice. The model used minimum travel costs as the optimization variable to determine the path to destination. Results showed that a tactical model was helpful in simulating pedestrian movement (validated from field observations). A principle of shortest perceived path is commonly used for pedestrian travel path modeling ( Borgers and Timmermans (1986) and Hoogendoorn and Bovy (2004) ). PAGE 35 35 Papadimitriou (2012) indicated that the preference of pedestri an travel path was a result of balancing the utility of following the shortest perceived path with the cost of carrying out many primary crossings, but no quantitative information on the cost of one primary crossing was provided in this research. Primary c rossing is defined as the crossing which is made at intersections or midblock crosswalks (with change of direction) for the purpose of following the particular route, which secondary crossing is made only at the intersections (without change of direction) while moving along sequential road links ( Lassarre et al., 2007 ) Figure 2 1 provides an example of primary and secon dary crossing. The existing pedestrian studies have contributed many insightful methods and results, but most of them were developed based on intersection/segment level. Pedestrian operations along travel path has not been well explored due to dynamic and quite complex pedestrian decision making process. Papadimitriou et al. (2009) identified the main difficulties for analyzin g that: explanatory approaches, flexible disaggregate modeling techniques and extensive data collection schemes. 2.5 Summary This chapter has briefly reviewed the advantages, limitations and applicability of models and methods in the literature regarding p edestrian operations in urban network from different perspectives. We conclude that in order to be applicable to a general urban network, there are three major issues identified for pedestrian operation analysis. 2.5.1 The Need f or Identifying Jaywalking B ehavior (Outside of Crosswalks) Pedestrian crossing outside of a marked or unmarked crosswalk (i.e. jaywalking), is one of those pedestrian behaviors that affect safety and operations. Pedestrian jaywalking behavior is commonly observed in the field, espec ially within an environment with high levels of pedestrian activities ( Zheng et al., 2015b ) Unlike permissible crossings at crosswalks, jaywalking events PAGE 36 36 are not often anticipated by drivers, which may result in lower driver reaction time, different vehicle dynamics, as well as different pedestrian operations ( Zheng et al., 2015a ; Zheng et al., 2015b ) Pedestrian jaywalking behavior may highly affect s the pedestrian route s election as well as the pedestrian trip travel time. To date, limited quantitative and behavioral research has been conducted to investigate this interaction or simulate it microscopically. 2.5.2 The Need f or Analytically Estimating Pedestrian Delay a t Uns ignalized Intersections Findings from observational studies showed some elements that had great impacts on pedestrian delay, such as platooned traffic ( Schroeder et al., 2014 ; Sisiopiku and Akin, 2003 ) driver yieldi ng behavior ( Schroeder, 2008 ; Sun et al., 2003 ) pedestrian yield recognition ( Schroeder et al., 2014 ; Schroeder, 2008 ) But they are not currently considered in the pedestrian delay model. The existing models may not perform well in estimating pedestrian delay in cases of high level pedestrian activities, such as in major city CBD areas, campus areas, etc. 2.5.3 The Need f or a n Integrated Approach t o Estimate Pedestrian Travel Time a t Travel Path T he existing studie s seldom examined the possible impact s of multiple crossing alternatives on pedestrian crossing behavior, or how the pedestrian vehicle interactions affected the pedestrian route choice as well as overall travel time at the path level. They usually separat ed pedestrian walking and crossing when analyzing pedestrian traffic operations in urban networks. However these may often be interrelated, and thus it is necessary to link the pedestrian movement and crossing behaviors with consideration of pedestrian veh icle interactions. Pedestrian travel time along travel path can be a good performance measure, since it captures the pedestrian perspective and considers the time spent along the travel path including crossing at intersections, walking along the links and interacting with other road users. Travel PAGE 37 37 time estimation can offer an integrated way to analyze pedestrian operations along the travel path and evaluate facility performance. PAGE 38 38 F igure 2 1 Schematic of Pedestrian Primary an d Secondary Crossing s PAGE 39 39 CHAPTER 3 MODELING PEDSTRIAN VEHICLE INTERACTIONS OUTSIDE OF CROSSWALKS This chapter establishes several quantitative relationships describing interactions between pedestrians crossing outside of crosswalks and approaching driver s using an instrumented vehicle experiment and an observational study on the campus of the University of Florida. The crossing speed, critical gap and yield acceptance between permissible crossings and jaywalkers, e two types of pedestrians were analyzed. The objective is to explore and quantity pedestrian jaywalking behaviors (crossing outside the crosswalks) and the corresponding driver yielding dynamics for modelling their interactions in a micro simulation envir onment for traffic operational analyses. The data collected and methods developed in this chapter provide the basis and assumptions that can be used within micro simulators to model those interactions. Section 3.1 provides an overview of the methodologica l framework for this research as well as the data collection for the instrumented vehicle study and the observational study. Section 3.2 presents the analysis results and findings with emphasis on pedestrian jaywalking behaviors and driver reactions. A sum mary of this chapter is provided in Section 3.3. 3.1 Meth odological Framework cs. The research team recruited subjects who then drove along two predetermined routes within the University of Florida campus. After that, an observational study was conducted to collect data at the high jaywalking frequency locations identified from the instrumented vehicle experiment. The details of each of the two data collection efforts are provided below. PAGE 40 40 3.1.1 Instrumented Vehicle Study The instrumented vehicle study enables real time recording of speed, location, etc., using a data acquisition sys tem ( Sun and Elefteriadou, 2012 ; Toledo et al., 2007 ) The instrumented vehicle used in this study is a Honda Pilot SUV, owned by the University of Florida Transportation Institute (UFTI). The vehicle has a built in GPS where all informat ion about vehicle position and speed data is displayed and recorded on a Honeywell Mobile Digital Recorder (HTDR400) system. The study team selected two routes on the campus in University of Florida, each with approximately 18 midblock crossings. The tota l distance of Route 1 is 4.7 miles and the estimated travel time is 16 min. There are 17 midblock and 7 signal crossings along the route. The total distance of Route 2 is 2.8 miles and the estimated travel time is 20 min. There are 19 midblock and 7 signal crossings along the route. More pedestrian interactions exi st along Route 1 than Route 2. Figure 3 1 provides maps of the two routes. After IRB (Institutional Review Board) approval was obtained, 15 participants with varying driving characteristics were selected based on age, gender, driving experience, occupation, and vehicle ownership through a prescreening questionnaire ( Table 3 1 provides an overview of the participant characteristics). Data were collected on weekdays starting at 4:30pm. Each particip ant was asked to meet the researchers at a pre specified point. Upon arrival, a check in procedure was followed: driving survey. Drivers were not told about the exa ct objective of this study in advance, so that they were not looking for jaywalkers or pedestrians specifically during the experiments. One researcher accompanied each subject and took notes regarding driver behavior and traffic conditions. After the compl etion of each route, drivers were asked to complete a questionnaire PAGE 41 41 regarding their actions and choices throughout the route. Questions related to lane changing, yielding, and actions around pedestrian walkways, bikeways, and transit vehicles. After the co during the entire experiment. The total duration of each experiment was approximately one hour. The following data were collected for each participant and each rout e they drove: Vehicle trajectory (speed, acceleration), and vehicle yield/no yield decision to jaywalkers Traffic flow conditions and roadway environment 3.1.2 Observation Study At the locations where a high number of jaywalkers were observed from the instrumented vehicle study ( Figure 3 2 ), the research team conducted a follow up observational study of pedestrian behavior at the same time period as the in vehicle study (weekdays from 4:30pm). The obs ervation duration at every location was 45 minutes (3 times of 15 minute period). A total of 487 jaywalking events were observed. The following data were collected at each location, and based on those, the average jaywalker, pedestrian and traffic volumes were obtained: Number of jaywalkers per minute Number of pedestrians (both crossing directions) per minute Number of vehicles (both directions) per minute Pedestrian and jaywalker characteristics (speed, delay) 3.2 Data Analysis This section provides the data analysis results related to vehicle pedestrian interactions outside the crosswalks. The VJI framework is firstly introduced and then the pedestrian behavior as well as the driver behavior reacting to them are analyzed separately in the scope of the fr amework. PAGE 42 42 3.2.1 Vehicle Jaywalker Interaction Framework A framework for the vehicle jaywalker interactions is shown in Figure 3 3. The presence of jaywalkers triggers the vehicle reactions and the driver starts to make a yield/no yield decision. As he/she d etermines the yield choice, the vehicle proceeds with the corresponding dynamics (keep car following, stop as a leading vehicle, soft yield, etc.). Data were collected to model the VJI, from the pedestrian perspective, observe where pedestrians are more li kely to jaywalk, and measure the crossing speed and the corresponding driver behaviors; from the driver perspective, to observe and quantify the driver yielding behavior, including the probability of yielding, likely location, and vehicle trajectories afte r a yielding or no yielding decision. The results are provided in the following sections. 3.2.2 Jaywalking Behaviors A jaywalking event is defined as a pedestrian crossing more than 10 feet outside of a marked or unmarked crosswalk at an intersection, or 10 feet outside of a marked midblock crosswalk. As specified by 2015) jaywalkers (crossing a roadway at any point other than within a marked crosswalk or within an unmarke d crosswalk at an intersection) shall yield the right of way to all vehicles upon the roadway. Other than that, a pedestrian crossing at marked or unmarked crosswalks is defined as a permissible crossing. The pedestrian jaywalking behaviors considered in t his study includes crossing location and surrounding roadway environment, pedestrian crossing speed, yield recognition and wait time. 3.2.2.1 Jaywalking l ocations and e nvironment c haracteristics Through the instrumented vehicle experiment, most jaywalking events (72.5%) were found to occur at specific locations ( Figure 3 2 ). Others were randomly located along the two routes. Among the five locations identified in Figure 3 2 Location 5 had the highest probability of a jaywalking event ( 40 %), i.e. there was a 40 % frequency in encountering a jaywalker when PAGE 43 43 passing through this location during the hour of analysis. The frequencies for Location 1 to 4 are: 13.33%, 16.67%, 20%, and 10% respectively. Operations were observed at each of these locations to collect j aywalker rates, pedestrian and vehicle volume (per minute), crossing distance and number of bus stops. The results of the data collection are shown in Table 3 2 On site observation indicated that jaywalkers are more likely to perform single stage crossing s even when there is a median. Jaywalkers seem to select gaps that are acceptable at all the lanes simultaneously. The data were analyzed to evaluate the correlations of those traffic and environmental variables with the observed jaywalker volume (from ob servational study) and the number of encountered jaywalking events (from instrumented vehicle study). Results (Table 3 3 ) indicate that: There is a high correlation of jaywalking events between the instrumented vehicle study and the field observations (0.9 37 correlation at 95% confidence), which indicates the results from the two studies are consistent; Pedestrian volume along the sidewalk has a significant impact on the number of jaywalkers (0.794 correlation at 95% confidence); The presence of bus stops r esults in more jaywalking events, since people are more likely to cross to or from their destinations; Crossing distance and vehicle volume have negative correlation to jaywalking frequency. her traffic volume reduces the vehicle headway and gap availability; The number of jaywalking events has a positive correlation with the distance between crosswalks. Pedestrians prefer to cross illegally if the crosswalks are too far away. 3.2.2.2 Jaywalk ing crossing speed Pedestrian crossing speed is one quantitative measure of pedestrian crossing behaviors and has been explored by several prior studies ( Fitzpa trick et al., 2007 ; HCM, 2010 ; MUTCD, 2009 ; STRIDE, 2012 ) For instance, the HCM 2010 ( HCM, 2010 ) assumes 4.0 ft/s as the defa ult PAGE 44 44 value of pedestrian average speed in all traffic/geometry/treatment conditions (i.e. signal intersection and midblock crosswalks). However, little previous research was found that has examined the pedestrian crossing speed outside the crosswalks, or an y differences with permissible crossings. Figure 3 4 provides the probability distributions of pedestrian speeds on campus (permissible crossings and jaywalking). There were a total of 343 permissible crossing observations and 487 jaywalker observations. T he analysis indicates the average permissible crossing speed on campus is 5.05 ft/sec, while the value for jaywalkers is 5.18 ft/sec for jaywalkers. There is no significant difference between these means based on statistical analysis. However, as shown in Figure 3 4 b, jaywalkers are more likely to run and the distribution of jaywalker speed is much flatter. The standard deviation for permissible crossings is 0.66 ft/sec, while for jaywalkers it is 1.65 ft/sec. There is higher variability in crossing speed o utside the crosswalks. Jaywalkers crossing when vehicles yield or during shorter gaps would prefer to walk faster; jaywalkers crossing during large gaps do not need to cross in a hurry, resulting in low crossing speeds. As expected, the average crossing sp eed on campus for both permissible crossings and jaywalkers is higher than the default value in the HCM 2010 (4.0 ft/sec for all ages and genders nationwide) ( HCM, 2010 ) 3.2.2.3 Jaywalking yield recognition Drivers have three options when encountering a crossing pedestrian: No Yield (NY), Hard Yield (HY), and Soft Yield (SY). Hard yield means that the vehicle slows down to complete stop for pedestrians, while soft yield means that the vehicle slows down without a full stop. The pedestrian yield recognition was observed in this rate is important when modeling or simulating pedestrian behavior and VPI/VJI, and it helps to more realistically rep licate the pedestrian delay, vehicle delay, etc. PAGE 45 45 As observed in this study, pedestrians crossing at crosswalks and outside the crosswalks have different expectations towards driver yielding. It was found that in permissible crossings at crosswalks, pedestr ians would accept all yields (100%), no exceptions. But jaywalkers prefer to cross during larger gaps rather than during yields ( Mitman et al., 2008 ) Their HY utilization rate is 98.33%, and SY rate is 91.67%. The lower yield utilizati on rates of both hard and soft yields yields. Meanwhile, the HY utilization rate is higher than that the SY one, which is consistent with former studies pe ople are more likely to accept a hard yield rather than a soft yield. Driver yielding behavior is discussed in a later section. 3.2.2.4 Jaywalking delay at the c urb Pedestrian delay at the curb (the time difference between their arrival at crossing point a nd starting to cross) was observed in the study. The average delay of jaywalkers is 0.87 sec, and much lower, because jaywalkers can make crossing decisions ( look for gaps) while still walking. 3.2.2.5 Summary on jaywalking b ehaviors The following observations are made with respect to jaywalking behaviors: Jaywalking events are concentrated around 5 locations along the two routes tested. The location with the h ighest number of jaywalking events has the highest pedestrian volumes along the sidewalk, a short crossing distance and two bus stops in the vicinity; Roadway environment characteristics of each jaywalking location are correlated to jaywalking events: pede strian volume, number of bus stops and distance between crosswalks have positive correlation; vehicle volume and crossing distance have negative correlation; The average pedestrian crossing speed outside the crosswalks is not significantly different from p ermissible crossings at the crosswalks (5.18 ft/sec and 5.05 ft/sec). However, there is more variability among jaywalker crossing speeds, which is represented by a flatter distribution and a higher standard deviation. The speed distributions can be used fo r replicating pedestrian operations in simulators; PAGE 46 46 Pedestrians crossing outside the crosswalks do not always accept all the driver yields. They have lower HY and SY utilization rates than permissible crossings (the latter accepts all the HY and SY); As exp ected, the average wait time of jaywalkers is significantly lower than that of permissible crossings. 3.2.3 Driver Reactions Jaywalking events are unexpected for drivers along their trip and they may not anticipate to yield to pedestrians away from crosswa lks. According to previous research ( Schroeder and Rouphail, 2010a ; Schroeder, 2008 ; Sun et al., 2003 ) their yield/no yield decision is made based on traffic conditions, pedestrian characteristics, driver characteristics, etc., similarly to driver yielding models for permissible crossings. Also, hard yield vs. s oft yield depends on the vehicle deceleration rate and the distance to the jaywalker crossing point. This section describes driver reactions to jaywalkers using data from the instrumented vehicle study. The driver reactions considered here include the yiel d rate, vehicle speed distance at the decision point (i. e., the decision to yield or not), and yield dynamics. 3.2. 3 .1 Driver yield rates The average driver yield rates were measured during the in vehicle study: the rate of yielding to jaywalkers is 50.67 %, while to permissible crossings it is 72.66%. These average rates are represented by the dash dot line in Figure 3 5 A total of 80% of the subjects indicated in the surveys (they answered during the in vehicle study) that they were aware of the local la ws regarding right of way at pedestrian crossings. As expected, drivers are much more likely to yield to pedestrians at marked crosswalks (permissible crossings). In addition, a comparison of driver yield behaviors to jaywalkers and permissible crossings w as conducted next. As discussed in another paper ( Zheng et al. 2015b ) yielding behavior to pedestrians at marked crosswalks can be applied as one effective measure to PAGE 47 47 classify driver types within a high level of pedestrian activity environment. In that paper, drivers were categorized into 4 types using a yield behavior based scheme ( Zheng et al., 2015b ) with gro up 1 being the least aggressive and 4 being the most aggressive. Driver yield rates (%Yield) with their respective driver type (x axis) are shown in Figure 3 5 with straight lines as linear regressions ( Figure 3 5 a the %Yield to jaywalkers, Figure 3 5 b the %Yield to permissible crossings). It is found that compared with permissible crossings, yielding to jaywalkers seems to data. Drivers do not anticipate to encounter with a jaywalking event, so that when encountering environment (speed, distance, jaywalker volume) rather than the driver attitudes. The surveys also indicated that 53% of the subjects mentioned (unprompted) specifically the existence of jaywalkers on campus and felt unsafe because of them. Although over half of the subjects reported the existence of jaywalkers, the No Figure 3 6 a and Figure 3 6 b). The average %No rate is independent of whether drivers mentioned the presence of jaywalkers in our survey. It could be that the yield/no yield reaction is more related to specific traffic and roadway environment conditions. It could also be that drivers who mentioned jayw alkers are more sensitive to their presence for other reasons. Based on the analysis of driver yield rates, it is found that driver yielding behaviors to jaywalkers are independent with their overall aggressiveness and awareness of jaywalkers. The PAGE 48 48 potenti al impacts of vehicle speed/distance on driver yield behaviors were thus explored in the next section. 3.2.3.2 Driver d ecision point and d istance s peed r elationship The driver decision point is defined to be the location where the driver starts to react to the presence of pedestrians. At that point, he/she decides to yield/no yield to the pedestrians waiting at the curb or currently crossing during a pedestrian crossing event. For each VPI and VJI, the driver decision point was processed based on the GPS da ta from the instrumented vehicle study. The average distance between driver decision point and jaywalkers is estimated to be 85.81 ft, while the average distance for permissible crossings is 132.37 ft. A statistical test of means indicates that these two distances are significantly different drivers have a much shorter reaction time to jaywalkers than to permissible crossings. This result also supports the finding that drivers have a lower probability of yielding to jaywalkers than to pedestrians at mark ed crosswalks. The vehicle speed at decision point was also obtained and the distance speed relationship at that point for all the yielding decisions (i.e. HY, SY, and NY) to jaywalking events is provided in Figure 3 7 It is clear that the yield decision can be classified by the distance speed relationship. The drivers are more likely to hard yield to jaywalkers if their speed is low and they are quite close to the crossing point at the time they make a decision. Drivers with higher approaching speed decid e to soft yield to jaywalkers if they are far away from the crossing point, otherwise they cannot stop and choose not to yield when the decision distance is short. This result points out the importance of vehicle distance and speed at the decision point, b oth of which highly affect driver reactions and vehicle trajectories towards jaywalkers. PAGE 49 49 3.2.3.3 Vehicle dynamics Based on the discussions on driver yield rates to jaywalkers and the distance speed relationship at decision point, the vehicle dynamics (dist ance speed profile) can be obtained to further analyze driver reactions and the vehicle trajectories. The distance speed profiles for the three decisions to jaywalking events (NY, HY and SY) are shown in Figure 3 8 As shown, in general, high speed and lon for drivers to stop completely, and the speed and distance cause of SY decision is in between (HY and NY). The deceleration rates for the three types are significantly different: NY ve hicles did not slow down, but stayed in car following mode; SY vehicles decelerated, but did not stop and started to accelerate after passing the pedestrian crossing point; HY vehicles had the highest deceleration rate and finally slowed down to a speed lo wer than 5 mph (considered as a stop). Next, this research further analyzes vehicle HY dynamics and SY dynamics in detail, which would help modeling vehicle operations in micro simulation. The NY vehicles stay in car following mode and there is no large d ifference between VPI and VJI, thus the vehicle NY dynamics are not further analyzed in this research The speed profiles for vehicles tha t perform HY and SY are analyzed within a distance of 100 ft, considering that the average driver decision point for j aywalking events is 85.81 ft. The vehicle dynamics in the presence of pedestrians are classified according to Time To Conflict (TTC): less than 4 sec, 4 to 6 sec, 6 to 8 sec, 8 to 10 sec and more than 10 sec. TTC is determined at the driver decision point the distance to the crossing point divided by the speed at that moment. The mean speed is estimated and plotted in Figure 3 9 (SY) and Figure 3 10 (HY) for each TTC condition for every 10 ft. Soft y ield As defined, SY vehicles do not necessarily have a complete stop, they prefer to decelerate and coast towards the crossing pedestrians. As shown in Figure 3 9 the vehicles PAGE 50 50 that choose to soft yield have different initial speeds, but they mostly share a similar deceleration rate the slopes are much flatt er than the HY one ( Figure 3 10 ). A statistical regression analysis was conducted to estimate the vehicle SY deceleration rate corresponding to different TTC and distance (results are shown in Table 3 4) A regression line (dash line) is also plotted in Fi gure 3 9 and indicates that the average deceleration rate is approximately 0.818 ft/sec 2 through the vehicle travel distance. The SY dynamics to permissible crossings were processed as well. The average SY deceleration rate is approximately 1.3 ft/sec 2 t hrough the vehicle travel distance. The simplified speed time profiles of VPI and VJI are shown in Figure 3 11 with a starting speed of 20 ft/sec. It is obvious that the drivers tend to slow down more to permissible crossings than to jaywalkers resulting in a lower coasting speed towards pedestrians at marked crosswalks. Hard y ield As defined, HY vehicles proceed to a complete stop in front of the crossing jaywalkers/crosswalks. As shown in Figure 3 10 the vehicles that choose to hard yield, have the si milar deceleration rates as they approach the jaywalker regardless of TTC. A statistical regression analysis was conducted to estimate the vehicle HY deceleration rate corresponding to different TTC and distance (results are shown in Table 3 4 ). A regressi on line (dash line) is also plotted in Figure 3 10 The average dece leration rate is approximately 3.27 ft/sec 2 The average HY deceleration rate is 3.4 ft/sec 2 which is not significantly different from the HY deceleration rates to jaywalkers. The simpl ified speed time profiles of VPI and VJI are shown in Figure 3 12 with a starting speed of 15 ft/sec. 3.2.3.4 Summary on driver r eactions We can conclude the following with respect to driver reaction to jaywalkers: Driver yielding rates are higher for pede strians in permissive crossings (72.66%) compared to jaywalking events (50.67%); The average yield rate to jaywalkers on campus is about 51%, and does not differ PAGE 51 51 reported to jaywalker behaviors are not influenced by their driver type as classified based on level of aggressiveness; Speed and distance at the driver decision point highly correlate to jaywalkers. The decision point determines the start (time) location of vehicle jaywalker interactions. It is shown that the decision point for reacting to jaywalkers is approximately 85.81 ft, while the average distance for permis sible crossings is 132.37 ft. Detailed vehicle SY and HY dynamics are obtained corresponding to different TTC to jaywalkers. The simplified models for both are developed and can be applied into micro simulators. 3.3 Findings and Discussions This research investigated jaywalking behavior as well as driver reaction to jaywalkers on the University of Florida campus. The objective of the research was to quantify driver and pedestrian behaviors as well as to model their interactions outside of designated cross walks. Data were collected through an instrumented vehicle study and an observational study. Firstly, the pedestrian crossing behavior outside the crosswalks was examined. Consistent with past studies, it was found that the locations where pedestrians ar e more likely to cross outside the crosswalks are highly influenced by the surrounding roadway environment and characteristics, such as pedestrian volume, number of bus stops, vehicular volume, distance between crosswalks and crossing distance. Significan t differences were observed between jaywalkers and pedestrians during permissible crossings in: crossing speed distribution, yield Yield and Soft Yield), res ulting in an overall lower yield utilization rate. Next, driver reactions to jaywalkers were examined. Driver yielding decision point to jaywalkers is closer to the crossing point, and the average yield rate to jaywalkers is lower than that to pedestrians at permissible crossings. It was also observed that drivers decelerate more for PAGE 52 52 pedestrians within a crosswalk than for jaywalkers. These differences may in return affect jaywalker behaviors. This research points out the specific jaywalking and vehicle re action behaviors, establishes quantitative relationships of VJI, and provides the basis and assumptions for modeling VJI/VPI in a micro simulation environment based on the data and observations in this study. Research implications and recommendations for f uture work are as follows. The jaywalker crossing speed distribution can be used within micro simulation packages when replicating jaywalker operations; The pedestrian delay at the curb collected in this study can be used to validate the simulation results ; The distance speed relationship at driver decision point can be used for yield choice modelling with further statistical analysis (cluster analysis, etc.) and then applied in simulation; The simplified models of vehicle soft yield and hard yield dynamics refine the vehicle operational performance and provide the basic algorithms that can be implemented in a micro simulator; The methodology developed for data collection and analysis, as well as the trends and insights in these from the data collected can b e used to develop larger scale studies for generalizing the results reported here. The data and methods developed can also be implemented in micro simulators which require detailed trajectory information of both vehicles and pedestrians; The yield recogni tion rate, can be used to develop jaywalker delay models for planning level applications (for example, when determining the optimal path a pedestrian may take, and consequently the attractiveness of jayw alking at a specific location.). The findings from t his study have implications related to research, planning, and engineering solutions for future work on pedestrian safety, crosswalk design and location, as well as modeling of driver behaviors for traffic operational analyses. They can also be used as the basis to formulate planning and engineering strategies to minimize jaywalking. PAGE 53 53 A B Figure 3 1 Maps of Two Study Routes for the Instrumented Vehicle Data Collection. A) Route #1, B) Route #2 PAGE 54 54 F igure 3 2 Observed Jaywalking Locations Route #2 Route #1 PAGE 55 55 A B Figure 3 3 Vehicle Jaywalker Interactions Framework. A) Vehicle Process Flow, B) Pedestrian Process Flow. PAGE 56 56 A B Figure 3 4 Frequency Distributions of Pedestrian Speeds. A) Permissible Crossings, B) Jaywalkers PAGE 57 57 A B Figure 3 5. Driver Yield Rates to Jaywalkers and Permissible Crossings. A) Yield Rates to Jaywalkers, B) Yield Rates to Permissible Crossings PAGE 58 58 A B Figure 3 6 Percentage of NY, SY, and HY Behaviors. A) Jaywalke r Reported Drivers, B) Jaywalker Unreported Drivers PAGE 59 59 Figure 3 7 Distance Speed Relationship at Driver Decision Point of HY, SY and NY For Jaywalking Events PAGE 60 60 Figure 3 8 Speed vs. Distance (HY, SY, NY). PAGE 61 61 Figure 3 9 Vehicle SY Dy namics (Dis tance Speed Profile). 0 5 10 15 20 25 30 100 90 80 70 60 50 40 30 20 10 0 Speed (ft/s) Distance (ft) <4 4~6 6~8 8~10 >10 Regression Line PAGE 62 62 Figure 3 10 Vehicle HY Dynamics (Distance Speed Profile). 0 5 10 15 20 25 30 100 90 80 70 60 50 40 30 20 10 0 Speed (ft/s) Distance (ft) <4 4~6 6~8 8~10 PAGE 63 63 Figure 3 11 Simplified SY Reaction to Jaywalkers and Permissible Crossings. PAGE 64 64 Figure 3 12 Simplified NY Reaction to Jaywalkers and Permissible Crossings. PAGE 65 65 Tabl e 3 1 Overview of the Participants and Their Characteristics Characteristics Number of Participants Percentage of Participants Age <25 2 13.33% 25 35 9 60.00% 35 45 1 6.67% 45 55 2 13.33% >60 1 6.67% Gender Female 7 46.67% Male 8 53.33% Identification Group Caucasian 8 53.33% Hispanic 4 26.67% African American 3 20.00% Driving Hours per Week <4 3 20.00% 4 8 6 40.00% 8 14 4 26.67% >14 2 13.33% Total 15 100% PAGE 66 66 Table 3 2 Traffic and Environmental Variables for Each Jaywalking Location Location 1 2 3 4 5 Jaywalker Volume (/min) 1.467 0.733 2.933 1.667 4.033 Average Pedestrian Volume Along the Sidewalk (/min) 1.8 2.333 2.55 3.233 5.633 Average Traffic Volume (/min) 6.1 5 5.583 1.367 2.95 Crossing Distance (ft ) 40 45 35.5 40 38.5 Nearby Bus Stops 1 0 1 2 2 Distance Between Crosswalks on Either Side of This Location (ft) 360 444 1023 747 487 Median No Yes No No No Comment Parking Lot Parking Lot Food Plaza Note: The crossing distance of Location 2 is the total lane width of both directions plus the median size. PAGE 67 67 Table 3 3 Correlation Analysis of Traffic and Environmental Variables Jaywalker Volume Pedestrian Volume Traffic Volume Crossing Distance Nearby Bus Stops Distance Between Crosswalks % Jaywal king Events Jaywalker Volume 1 Pedestrian Volume 0.794* 1 Traffic Volume 0.224 0.620 1 Crossing Distance 0.744* 0.249 0.013 1 Nearby Bus Stops 0.639 0.681 0.735 0.547 1 Distance Between Crosswalks 0.303 0.042 0.126 0.670 0.196 1 % Jaywalking Events 0.937* 0.926* 0.337 0.472 0.555 0.124 1 Note: 95% confidence leve l PAGE 68 68 Table 3 4 Vehicle Deceleration Rate (ft/sec 2 ) in Yielding Behaviors Driver Reactions TTC (sec) < 4 4~6 6~8 8~10 > 10 Soft Yield 0.422 0.975 1.208 0.788 0.621 Hard Yield 3.963 4.180 3.127 2.664 2.555 PAGE 69 69 CHAPTER 4 MODELING PED E STRIAN DELAY AT UNSIGNALIZED INTERACTIONS IN URBAN NETWORKS Pedestrian delay, as a key performance measure for quantitatively evaluating the pedestrian vehicle interactions and the facility Level of Service, is not well estimated in the existing studies to sufficiently capture the realistic pedestrian street crossing behavior at unsignalized intersections in urban networks. This chapter provides an improved analytical model to mathematically estimate pedestrian delay, which considers driver yielding and vehicle platooning. The pedestrian delay model in this chapter is developed using Renewal Theory, which solves th is pedestrian street crossing problem in a direct way as a stochastic process and provides possibilities for future model expansion. Section 4.1 provides an overview of methodological framework on pedestrian delay estimation at unsignalized intersection i n urban networks. Section 4.2 discusses the model assumptions and provides the generalized model formulation along with two application cases. Section 4.3 presents the model validation procedure and results with field data Section 4.4 provides the expande d model validation with the stochastic simulation. A summary of this chapter is provided in Section 4.5. 4.1 Methodolog ical Framework Pedestrian street crossing leads to direct interactions with motor vehicles and other road users. Pedestrian crossing at u nsignalized intersections can be simply deconstructed as follows: A pedestrian arrives at an unsignalized intersection and desires to cross the major traffic stream. If the vehicle pedestrian gap (i.e., the time headway between th e pedestrian arrival and the (which is equal to the minimum time to cross the road), the pedestrian crosses the street immediately; if not, the pedestrian waits, and PAGE 70 70 the crossing probability depends on the driver yield behavior. A schematic of this problem is shown in Figure 4 1 as a time space diagram. Vehicle trajectories are presented ( is the time headway between vehicle i and i+1 ). Pedestria ns randomly arrive (at time ) at the curb and make a crossing decision immediately. The wait time at the curb (i.e., the time difference between pedestrian arrival t and departure ) is defined as the pedestrian delay for street crossing. The objective of this study is to propose a generalized mathematical model of pedestrian delay for crossing a traffic stream at unsignalized intersections, and based on that to address driver yielding and platooned vehicular traffic conditions in urban networks. The model is developed using Renewal Theory, which solves this problem in a more direct way as a stochastic process and provides possibilities for future model expansion. Firstly, a generalized model is developed to be applied with any v ehicle headway distribution or driver yield behavior assumptions (solving a G/G/1 queuing system). Then the proposed model is applied on the basis of a mixture of free traffic and platooned traffic with consideration of driver yielding behaviors to replica te field conditions. A special case adopting the HCM 2010 assumptions is also derived as a comparison with the HCM 2010 model. Next, the model was compared to field data. A total of 110 pedestrian crossing events in Gainesville, Florida, as well as 99 pede strian crossing events in Washington, D.C., were used in the comparison. An expanded validation using simulation was also employed to evaluate the model results under a broad set of parameters. 4.2 Model Formulation This study provides a mathematical appro ach of estimating pedestrian delay for street crossing at unsignalized intersections in urban networks. The interaction between the waiting pedestrian and the first approaching vehicle is considered. Once the vehicle passes the pedestrian PAGE 71 71 crossing location (i.e. the pedestrian fails to cross), a new interaction arises between this pedestrian with the next approaching vehicle. For each pedestrian vehicle interaction, the pedestrian encounters one of the three scenarios shown in Figure 4 2 and experiences the corresponding pedestrian delay. Renewal theory is a branch of probability theory that generalizes stochastic processes. Renewal process is a counting process that captures the number of occurrences in a particular duration where the inter arrival times be tween sequential occurrences are independent and identically distributed with an arbitrary distribution ( Ross, 1996 ) It is usually applied to solve complicated cases that have randomly occurring events at which the system returns to a state probabilistically equivalent to the starting state ( Gallager, 2013 ) The Poisson process is a special case of renewal process in which the inter arrival times between renewals ha ve an exponential distribution ( Smith, 1958 ) A delayed renewal process represents the case when the first inter arrival time has a different distribution than the rest of the inter arrival times. In other words, t he ordinary renewal process is delayed, i.e., it starts after the epoch of the first renewal. In terms of the pedestrian street crossing at unsignalized intersections in urban networks it can be treated as a delayed renewal process with vehicle arrivals a s random occurrences. Upon arrival, the time difference between the arrival of a pedestrian and the next vehicle is regarded as the first renewal, which may have different distributions from the rest of the vehicle headways. The distribution, moment functi on, as well as the mean and variance of pedestrian delay can be directly derived. We assume that the vehicular headway in the traffic stream is distributed with probability distribution function The pedestrian arrives at time and the time difference between PAGE 72 72 the arriving pedestrian and the closest vehicle in the traffic stream is called pedestrian By renewal theory, t he probability distribution of the first inter arrival can be derived as follows ( Weiss and Maradudin, 1962 ) : (4 1) A generalized model is first developed that can be applied to arbitrary vehicle headway distributions and vehicle yielding behavior as sumptions, and then the proposed model for estimating pedestrian delay in urban networks is provided (assuming Cowan M3 for vehicular headway distribution, as it was recommended in the past studies for applying in urban networks ( Akcelik and Chung, 1994 ; Vasconcelos et al., 2012 ) ): Platooned traffic flow is defined to occur when a vehicle follows another vehicle at a constant headway Free flowing traffic is define d to occur when vehicles are travelling at headways larger than The model assumptions are as follows: Pedestrians are crossing one traffic stream (one lane crossing or multiple lane traffic is considered as one stream). Pedestria n behaviors are consistent and homogeneous: identical critical gap (crosswalk length divided by cross speed); pedestrian gap acceptance rate = 100%, if pedestrian vehicle gap ; pedestrian yield acceptance r ate = 100%, if vehicle yields. Upon arrival at the curb, the pedestrian immediately makes a crossing decision. Vehicle headways are independent, identically distributed random variables with probability density function. Vehicle yield probability is a function of the corre sponding vehicle pedestrian gap: Vehicles will not be able to yield if the gap is less than the safely yielding time distance ( is determined by the vehicle sp eed and maximum braking deceleration rate); Vehicles will yield with a constant value y (no more than 1), if the gap is between the vehicle minimum headway and pedestrian critical gap PAGE 73 73 Each vehicle pedestrian interaction is independent. Vehicles and pedestrians are treated as points, without considering vehicle length or pedestrian body width. The variable definitions and notations are as follows: : Pe destrian arriving time for pedestrian i (sec) : Pedestrian departing time for pedestrian i (sec) : Vehicle headway for vehicle i (sec) : Distance between the pedestrian and the c losest approaching vehicle (sec) : Pedestrian critical gap (sec) : Vehicle arrival rate (veh/sec) : Vehicle safely yielding distance (sec) (i.e., the minimum distance for making a safe stop) : Pedestrian reaction time to driver yields (sec) : Vehicle headway for platooned traffic (sec) (Cowan M3) : Proportion of free traffic (Cowan M3) : Probability distribution function of vehicle headways : Probability distribution function of vehicle yield rate (4 2) : Probability that the pedestrian accepts the v ehicle pedestrian gap (4 3) : Probability that the pedestrian crosses the street : Probability of accepting the first vehicle pedestrian lag PAGE 74 74 (4 4) : Probability of accepting the next vehicle pedestrian gap (4 5) : The expected pedestrian delay under renewal process (sec) : The expected pedestrian delay under ordinary renewal process (sec) : The wait time conditional on crossing in the first vehicle pedestrian lag (sec) : The wait time conditional on crossing in the next vehicle pedestrian gaps (s ec) : The expected pedestrian gap delay under renewal process (sec) : The expected pedestrian yield delay under renewal process (sec) 4.2.1 Generalized Model A generalized model is provided to accommoda te different traffic conditions including any vehicle headway distributions, any assumptions of vehicle yielding behavior, pedestrian yield recognition behavior, and pedestrian gap acceptance behavior. The only assumption in this model is independent vehic le pedestrian interaction. We define as the probability of pedestrian gap acceptance, which is a function of the corresponding vehicle pedestrian gap. Then, the probability of pedestrian street crossing is as follows: (4 6) We further define as the expected pedestrian delay time under this renewal process and define as the wait time for crossing under ordinary renewal process. is obtained PAGE 75 75 by estimating the wait time conditional on crossing in the first vehicle pedestrian lag ( ) and the wait time conditional on crossing in the subsequent gaps ( ). is estimated as the sum of the expected delay due to not crossing in the first vehicle is derived similarly. The estimations for and are as follows: (4 7) (4 8) is thus obtained as follows (refer to Appendix A for the detailed derivation): (4 9) The first part of can be treated as the expected pedestrian gap delay and the second part can be treated as the expected pedestrian yield delay It is noteworthy that in the case of ignoring driver yielding ( ) and assuming Poisson vehicle arrivals, the expected delay equation is derived from Equation (4 9) as follows, which is consistent with the delay equation developed by Adams (1936) : (4 10) PAGE 76 76 4.2.2 Proposed Model: Application to Urban Settings Two major assumptions are used and applied within the generalized model presented above to replicate u rban settings: Vehicle yield behavior is considered the driver yield rate depends on the corresponding time distance between waiting pedestrians at the curb and the approaching vehicle; Platooned traffic is considered the vehicle arrival distribution is assumed to be Cowan M3 model. In this case, the probability distribution function of Cowan M3 distributed vehicle headways is ( Cowan, 1975 ) : (4 11) Where is the dirac delta function, and is the proportion of free vehicles. Thus, according to Equation (4 1) the distribut ion of the vehicle pedestrian lag is derived as (refer to Appendix B for the detailed derivation): (4 12) The pedestrian crossing probability density function can be derived as (refer to Appendix C for the detailed derivation): (4 13) As the driver yielding probabilities and vehicle headways are both functions of vehicle pedestrian gap, it is necessary to distinguish the magnitude of the parameters for different cases. The next subsection presents the case when the vehicle is travelling at a low speed so that the minimum braking time distance is less than the vehicle platooned headway, while the second PAGE 77 77 subsection presents the case when the vehicle is tr avelling at a higher speed so that the minimum braking time distance is larger than the vehicle platooned headway. 4.2.2.1 Vehicle safely yielding distance is less than vehicle platooned h eadway ( ) When the vehicle is travelling a t a rather low speed, the minimum braking time distance may be less than the vehicle platooned headway. In this case, the probability of accepting the first vehicle pedestrian gap ( ) and the probability of accepting the next vehic le pedestrian gap ( ) can be derived by renewal theory (Equation (4 14) and (4 15) ) (refer to Appendix D and E for the detailed derivation): (4 14) (4 15) The expected pedestr ian delay time under this delayed renewal process ( ) is obtained by estimating the wait time conditional on crossing in the first vehicle pedestrian lag ( ) and the wait time conditional on crossing during subsequent gaps ( ). For in the case of the driver is not able to yield (the lag is less than the vehicle safely yielding distance) so that the pedestrian cannot cross. The expected wait time is the sum of the first lag ( ) plus the wait time under the ordinary renewal process ( ). In the case of the pedestrian can cross only if the vehicle yields. The expected wait time is the product of reaction time ( ) and driver yield probability ( ) (if the driver yields) plus the product of expected wait time ( ) and driver no yield pro bability ( ) (if the driver PAGE 78 78 does not yield). In the case of the pedestrian can cross immediately. The expected wait time is zero. is estimated as follows: (4 16) Similarly, the wait time conditional on crossing in the subsequent gaps ( ) is estimated as follows: (4 17) The total expected delay ( ) is thus derived from the ge neralized model (Equation (4 9) ) as follows (refer to Appendix F for the detailed derivation): (4 18) The first part of can be treated as the expected pedestrian delay for crossing during a gap and the second part can be treated as the expected pedestrian delay due to reaction time for crossing during a yield PAGE 79 79 4.2.2.2 Vehicle safely yielding distance is larger than vehicle platooned h eadway ( ) When the vehicle is travelling at a high speed, the minimum braking time distance may be larger than the vehicle platooned headway. In this case, the probability of accepting the first vehicle pedestrian gap ( ) and the probability of accepting the next vehicle pedestrian gap ( ) can be derived by renewal theory (as presented in Appendices D and E): (4 19) (4 20) Similar to the mode l formulation in section 4.2.1, the expected pedestrian delay is estimated as follows with the first part as the expected delay for crossing during a gap and the second part as the expected delay due to reaction time for crossing d uring a yield (refer to Appendix G): (4 21) PAGE 80 80 4.2.3 Application Adopting the HCM Assumptions: Comparison to the HCM 2010 Framework The HCM 2010 assumes the vehicle arrivals are Poisson distributed (vehi cle headways follow the negative exponential distribution) and the driver yield rate is independent with a constant value. Using those assumptions, the pedestrian crossing probability density function becomes: (4 22) Then the expected pedestrian delay is derived from Equation (4 18) (with ) as follows: (4 23) (4 24) Whe re (4 25) The expected pedestrian delay ( ) is estimated as: (4 26) The pedestrian delay model used in the ( HCM, 2010 ) with the same assumptions is as follows: PAGE 81 81 (4 27 ) Where average number of crossing events before an adequate gap is available. This equation is a combination of theoretical and empirical work. A comparison of the two equations shows that under the same traffic condition, th e HCM 2010 model always overestimates the pedestrian delay compared to Equation (4 26) ( Figure 4 3 ). 4.3 Model Validation Using Field Data This section compares pedestrian delay obtained in the field to the delay estimated using the proposed model presente d in Section 4.2, the delay estimated using the derivation with HCM assumptions in Section 4.3, and the delay estimated using the current HCM 2010 model. Two midblock crossings with marked crosswalks were selected for observation (one at Gale Lemerand Dr. in Gainesville, Florida, and one at Madison Dr. in Washington, D.C.). A total of 110 observations of naturalistic pedestrian crossings with 170 vehicle headways were collected in Florida and a total of 99 observations of naturalistic pedestrian crossings w ith 206 vehicle headways were collected in Washington D.C. The data collection procedure, the characteristics of both sites and comparison between observed delay and estimated delay by the proposed model are presented below. PAGE 82 82 4.3.1 Data Collection Two ca meras were set up near the midblock to capture the vehicle pedestrian interactions one was facing the crosswalk for recording the pedestrian crossing process, the other was facing the midblock upstream for recording the approaching vehicle operations. A variety of data were collected based on the video recordings, including the vehicular volume, the percentage of driver yielding, and the pedestrian arrival and departure time at the crosswalk. The average pedestrian crossing speed and the pedestrian delay were then calculated for comparison with the results from the proposed model. In our data analysis we assume the following: The pedestrian was aware of the approaching vehicle and made a crossing decision based on the gap and vehicle yielding behavior. T he driver was aware of the pedestrian and reacted accordingly. 4.3.2 Site Descriptions The first site is located at Gale Lemerand Dr., Gainesville, Florida (schematic shown in Figure 4 4 a). It is two lane road with a marked crosswalk (length is 60 ft) and median refuge island. The vehicle flow rate (bi directional) is 334 veh/h, and the pedestrian flow rate during the analysis hour is 100 ped/h. The vehicle average speed is 20 mph and the vehicle yield rate is 70%. The pedestrian walking speed is 4 sec/ft. The second site is located at Madison Dr., Washington, D.C. (shown in Figure 4 4 b). It is one lane road with a marked crosswalk (length is 30 ft) and on street parking. The vehicle flow rate (bi directional) is 611 veh/h, and the pedestrian flow rate duri ng the analysis hour is 198 ped/h. The vehicle average speed is 15 mph, and the vehicle yield rate is 42%. The pedestrian walking speed is 4 sec/ft. PAGE 83 83 4.3.3 Comparison Results Next, the field delay is compared to the delay predicted by the proposed model. We first obtain the vehicle headway distribution of each site in order to use it in the model. Figure 4 5a and Figure 4 5b provide the density plots for the two locations. The Maximum Likelihood Estimation (MLE) technique was used to obtain the unbiased es timator for each parameter in the vehicle headway distribution model ( Lu ttinen, 1999 ; Troutbeck, 1997 ) The Cowan M3 vehicle headway distribution was fitted for both sites with (critical ) and 1.587 (critical ) respectively. The value for each estimator at the two sites is shown in Table 4 1 The fitted distributions are also plotted in Figure 4 5a and Figure 4 5b Additional parameters were obtained from the on site observation or video. For e xample, the pedestrian reaction time to driver yields is estimated as the time difference between driver yielding and the waiting pedestrian starting to step into the crosswalk. The vehicle safely yielding distance is estimated using the average vehicle sp eed and assuming 30 ft/sec as the vehicle maximum braking deceleration rate ( Table 4 1 ). Table 4 2 provides a summary of the estimated and observed values. As shown, the observed pedestrian delays at the two sites match well with the estimated delay from t he proposed model there is no significant difference at the 95% confidence level. Numerical data in correct assumptions and well calibrated model parameters. Pedestrian delay at both si tes is also estimated using the derived HCM model (Equation (4 26) ) and the HCM 2010 model (Equation (4 27) ). Vehicle arrivals are assumed to be Poisson distributed and vehicle yield rates are constant as 70% and 42% respectively. Comparison results are sh own in Table 4 3. Statistical analyses indicate there are significant differences between PAGE 84 84 field data and those two model results: the derived HCM model underestimates the field data, while the HCM 2010 prediction approximately doubles the observed delay in the field. This comparison underscores the importance of applying correct model assumptions, and further validates the applicability of the proposed model in urban networks with platooned traffic and driver yielding behavior. To consider the validity of t he model outside the conditions prevailing at these study sites, next we use simulation to expand the scenarios considered, and we compare the simulated results to the model estimated delay. 4.4 Expanded Validation Using Simula t ion A simulator is develope d using MATLAB ( MATLAB, 2013 ) and initially compared to the field data to ensure its validity. Next, stochastic simulations that replicate different traffic conditions were conducted to further validate the pedestrian delay obtained from the proposed model. The following assumptions were made for the simulat ion to replicate the field conditions: A vehicle pedestrian interaction zone is defined. Vehicle pedestrian interaction occurs within this zone when the vehicle approaches the pedestrian crosswalks (i.e. the time distance is equivalent to pedestrian criti cal gap). For example, pedestrians definitely cross if the vehicle has not reached the edge of the interaction zone. In other words, the vehicle outside the interaction zone does not need to make a yield decision for waiting pedestrians. For simplicity, th e vehicles in this simulation are generated at the edge of the vehicle pedestrian interaction zone. The vehicle deceleration rate for yielding is assumed to be 10 ft/sec 2 and the acceleration rate for speeding up is assumed to be 5 ft/sec 2 Vehicles make one yield/no yield decision to each single vehicle pedestrian interaction. Vehicles can speed up to the initial speed right after the crossing pedestrians arrive at the opposite side of the crosswalk. Pedestrian arrivals are Poisson distributed. The pedes trian critical gap is determined by assuming the average pedestrian crossing speed as 4 ft/sec, and the crosswalk length is 16 ft. PAGE 85 85 A flow chart of vehicle pedestrian interactions used in the simulation is provided in Figure 4 6 The rectangles in the flow chart represent basic decision making; the ellipsoids represent models implemented in the simulation; the triangles represent final status in each time step. 4.4.1 Comparisons between Field Data and Simulation Results Assuming Cowan M3 distributed vehicle inter arrival headways, a total of 100 runs were conducted and the average pedestrian delays were obtained from the simulator. Results are shown in Table 4 4 A statistical analysis was also conducted and confirms that there is no significant difference i n the average pedestrian delays between field data and simulation results for both sites (95% confidence level). 4.4.2 Comparisons between Simulation and Proposed Model Results Six parameters (pedestrian volume, vehicular traffic volume, vehicle yield rat e, vehicle safely yielding distance, vehicle headway distribution, and pedestrian reaction time to vehicle yields) with the corresponding values were combined and tested with 100 runs for each scenario (one combination of these parameters is considered as a scenario). The simulation resolution was set as 0.01 second. Table 4 5 provides an overview of all scenarios tested. A total of 1200 scenarios (100 runs for each scenario) were simulated. Figure 4 7 provides the comparison results for pedestrian delay fr om the proposed model and from the simulation program in different combinations of parameters. The x axis represents the delay from the model and the y axis represents the delay from the simulation. As shown, the regressed trend line is with The simulation results support the validity and accuracy of the proposed model. The delay differences are within close agreement and are mainly due to stochastic deviations. PAGE 86 86 4.5 Findings and Discussions An analyt ical pedestrian delay model for pedestrian crossings at unsignalized intersections in urban networks was developed by using renewal theory. First, a generalized model was developed which can accommodate different traffic assumptions. Then the proposed mod el was developed by applying a suitable set of assumptions to estimate pedestrian delay with consideration of commonly observed driver yielding behavior and platooned traffic in urban settings. Another application was developed using the HCM assumptions, a nd it was concluded that the HCM 2010 model overestimates the pedestrian delay relative to the model developed using HCM assumptions. A data collection was conducted and the observed pedestrian delay in the field (Gainesville, Florida and Washington, D.C.) was compared with the results from the proposed model. It was concluded that the model replicated field observations very well (95% confidence level). Furthermore, a stochastic simulation was employed using MATLAB in order to evaluate the model performan ce for scenarios not encountered during the data collection. Combinations of different parameters in the model were tested and the simulated delay was compared to the delay estimated by the analytical model. The results confirmed the model validity (95% c onfidence level). In general, the analytical model developed in this study replicates well pedestrian delay in an urban setting and can be used for similar applications in the future. The major contributions of this study and recommendations for future ap plication are as follows: The proposed model can estimate reasonably well pedestrian delay for street crossing in an urban setting with platooned traffic stream and observed driver yield behavior; A generalized method is provided to mathematically estimat e the pedestrian delay time, without restricting the model to a particular vehicle headway distribution or driver yield behavior assumptions. It can be applied to various special cases by fitting in distributions or other parameters; PAGE 87 87 The application with H CM assumptions provided in this study is recommended as an analytical model for the HCM when the traffic pattern and driver behavior satisfy the HCM assumptions. The following are recommended for future research based on the study results: The vehicle p edestrian interactions may be correlated. In this case the pedestrian crossing problem may be solved by using the technique of Markov Chains; One of the major assumptions for the proposed model is that the driver yielding possibility is only dependent on t he distance between the approaching vehicle and the pedestrians. But the driver yield decision may be affected by the yield be havior of the vehicle in front ( Sch roeder et al., 2014 ; Schroeder, 2008 ) This restriction can be relaxed and future models with modified driver yielding functions can be developed based on the generalized model provided in this study; The other assumption employed in our model is that the pedestrian will always accept the gap if it is larger than the critical value. This restriction can be relaxed and future models with pedestrian gap acceptance distributions/models can be developed ba sed on the generalize d model provided in this study. PAGE 88 88 Figure 4 1 Schematic of the Pedestrian Delay Model Framework PAGE 89 89 Scenario Schematic Delay Crossing in Gap 0 Cros sing in Yield ; Vehicle Yields (constant) Failing to Cross ; Vehicle Not Yields (or physically cannot yield) Note: is the pedestrian arrival time, is the pedestrian departure time, is the first vehicle pedestrian lag, is vehicle pedestrian g ap, is pedestrian critical gap, is a constant value representing the pedestrian reaction time to driver yields. Figure 4 2. Pedestrian Vehicle Interaction Scenarios. PAGE 90 90 A B Figure 4 3 Comparison between the Derived HCM Model and the current HCM 2010 Model A ) Fixed vehicle yield rate y = 0.25 B ) F ixed pedestrian critical gap = 3.25 PAGE 91 91 A B Figure 4 4 Site Descriptions ( Reprinted with permission from Google Maps Onl ine, https://www.google.com/maps ( O ctober 23, 2015 ) ) A ) Site 1 (Gainesville, FL) B ) Site 2 (Washington, D.C.) PAGE 92 92 A B Figure 4 5 Density Plot and Fitted Distributio n for Vehicle Headway A ) Site 1 (Gainesville, FL) B ) Site 2 (Washington, D.C.) PAGE 93 93 A B Figure 4 6 Flow Chart of Vehicle Pedestrian Interactions at Unsignalized Intersections ( ( Schroeder et al., 2014 ) ) A ) Vehicle Perspective B ) Pedestrian Perspective PAGE 94 94 Figure 4 7 Pedestrian Delay from Proposed Model and Simulation PAGE 95 95 Table 4 1 Model Estimators Estimator/Site Site 1 (Gainesville, FL) Site 2 (Washington, D.C.) Vehicle Headway Distribution 0.97 0.92 0.05 0.22 2.28 1.70 Yield Rate 0.70 0 .42 Vehicle Safely Yielding Distance (sec) 1 0.73 Pedestrian Reaction Time to Yields (sec) 2 1 PAGE 96 96 Table 4 2 Pedestrian Delay Comparisons (Field Data & Proposed Model) Field Data Proposed Model P va lue Average (sec) Std. Deviation (sec) No. of Observations (#crossings in yield) Site 1 (Gainesville, FL) 0.64 0.43 132 (92) 0.58 sec 0.1096 Site 2 (Washington, D.C.) 3.42 1.25 99 (42) 3.40 sec 0.8728 PAGE 97 97 Table 4 3 Pedestrian Delay Comparisons (Fie ld Data & Proposed Model & Derived HCM Model & HCM 2010 Model) Field Data (sec) Proposed Model (sec) Derived HCM Model (sec) HCM 2010 Model (sec) Site 1 (Gainesville, FL) 0.64 0.58 0.53 2.22 Site 2 (Washington, D.C.) 3.42 3.40 2.79 5.33 PAGE 98 98 Table 4 4 Pedestrian Delay Comparisons (Field Data & Simulation). Site 1 (Gainesville, FL) Site 2 (Washington, D.C.) Field Data Average Delay (sec) 0.64 3.42 Std. Deviation (sec) 0.43 1.25 No. of Observations 132 99 Simulation Average Delay (sec) 0.62 3 .39 Std. Deviation (sec) 0.21 0.99 No. of Observations 100 100 P value 0.5156 0.6966 PAGE 99 99 Table 4 5 Simulation Scenarios Tested Variables Testing Scenarios Pedestrian Volume (ped/hour) 50 100 500 1000 1500 Vehicle Volume (veh/hour) 100 500 1000 1500 2000 Vehicle Headway Distribution Exponential Cowan M3 Vehicle Yield Rate 0 0.2 0.5 0.8 Vehicle Safely Yielding Distance (sec) 0 1.5 3 Pedestrian Reaction Time to Yields (sec) 0 2 PAGE 100 100 CHAPTER 5 MODELING PEDESTRIAN TRA VEL TIME ALONG TRAVEL PATH WITH CONSIDERATIONS OF VEHICLE INTERACTIONS This chapter provides a methodology to estimate pedestrian travel time along travel path with considerations of pedestrian vehicle interactions. We focus on p edestrian crossing location and pedestrian link delay. The objective is to obtain a comprehensive model to estimate pedestrian travel time at the path level for pedestrian operations evaluation purposes ; and such a model can also be used for predicting the travel time before the tri p. Section 5.1 provides an overview of the methodolog ical framework for modeling pedestrian travel time along travel path. Section 5.2 presents the data collection procedure and site description s Section 5.3 presents the model for determining pedestrian crossing location and the respective probability. Section 5.4 presents the model for estimating pedestrian link delay due to crossing opportunities and potential vehicle pedestrian interactions. Section 5.5 elaborates the overall pedestrian travel time est imation model along with a numerical example. A summary of this chapter is provided in Section 5.6 5.1 Methodological Framework Pedestrian travel time at the path level is a quantitative measure that includes pedestrian movement, crossing and pedestrian v ehicle interactions. Only a few studies analyzed this and these did not consider the possible vehicle interactions and the variabilities in pedestrian behavior. Therefore, to obtain a comprehensive model for pedestrian operations evaluation purposes, we pr opose developing a method to estimate pedestrian travel time at the path level. A data driven methodology is proposed. Recording pedestrians as they travel along their paths (an adaptation of the floating car method) with GPS recording the real time locat ion and travel speed is suggested as an approach to collect data. Data include pedestrian travel time at each component of the path, pedestrian crossing location (signal intersections, PAGE 101 101 unsignalized/midblock crossing, or jaywalking), pedestrian individual c haracteristics (gender, age), roadway characteristics (shoulder width, number of lanes, crossing facilities, signals), and traffic conditions (traffic volume, average travel speed). Distributions of overall pedestrian travel time as well as walking time an d delay time at each location can be obtained. First, a pedestrian crossing location selection model is developed using data from the field observations. A sequential model is fitted to predict the probability of crossing at different facilities as well as the expected crossing delay at one crossing link. Furthermore, the relationship/dependence between pedestrian movement and crossing behavior is examined by estimating the pedestrian link delay due to crossing opportunities and probabilities. Finally, the total travel time along travel path is estimated as the summation of expected crossing delay at each crossing link, link delay, and link walking time. Figure 5 1 shows the methodological framework. 5.2 Data Collection Pedestrian crossing data from three lo cations were collected: Gainesville, FL, Orlando, FL and Washington, D.C A total of 375 crossing events were collected. The f loating pedestrian method (an adaptation to floating car method) was used to collect the data using a data acquisition system. The participant randomly join the pedestrians and walk as the prevailing speed of the nearby pedestrians to complete the route with GPS device recording the speed and travel path. Once one route is completed, the participant randomly wait s for another pedestr ian platoon to start the next trial. Time periods for the data collection include peak and off peak for mornings and afternoons (each city has its specific peak time). Table 5 1 shows the data collection time and location for each city. Figure 5 2a is a sn apshot of the data collection app and Figure 5 2b shows one data example which was collected in Washington, D.C. In general, the following data were collected: Pedestrian trajectory, age, gender; PAGE 102 102 Pedestrian volume on the sidewalk, number of pedestrians in this following platoon; Vehicle volume; Road segment length, number of lanes, crosswalk width, signal timing; Time of day, day of week. 5.3 Crossing Delay Estimation Pedestrian crossing link along the travel path is firstly determined and the probability of each crossing choice is estimated. The crossing link here refers to the link/segment along the travel path which selected by the pedestrian. The crossing choice refers to the crossing facility along the selected link which chosen by the pedestrian, e.g. intersection crosswalk, or midblock crosswalk. 5.3.1 Crossing L ink There are two types of pedestrian crossing s defined along pedestrian travel path: primary crossing and secondary crossing. Primary crossing is defined as the crossing which is made at int ersections or midblock crosswalks with change of direction for the purpose of following the particular path, which secondary crossing is made only at the intersections without change of direction while moving along sequential road links ( Lassarre et al., 2007 ) For a particular pedestrian travel path ( Figure 5 3 ), Jordan Curve Theorem is used to classify each crossing li nk type First, Jordan curve is drawn according to the road and intersections along travel path. Jordan curve divides the space into two distinct regions, an interior region bounded by the curve and an exterior region containing all of the nearby and far a way exterior points Any path starting from one region to an other will intersect the curve ( Jord an, 1893 ) The primary crossing is the one intersects the curve, while the secondary crossing is the path inside either region (interior/exterior region ). The location of primary crossing is probabilistic, while the secondary crossing is deterministic ba sed on the location of primary crossings. That is to say, for a pedestrian trip, once the travel path is selected, the choice PAGE 103 103 sets for primary crossing links are determined (according to network geometry) and thus the secondary crossing links are determine d. Figure 5 3 shows the schematic of those two types of crossings and Jordan curve 5.3.2 Crossing Probability Pedestrian crossing choice model captures the location that pedestrian selects to cross. The crossing choices at a particular link include cross walks at signal intersections, midblock crossings, jaywalking locations if possible. Pedestrian may not have full information on the available crossing choices along the travel routes, or may not consider all the crossing choices simultaneously. A sequenti al choice model is thus built and the pedestrian crossing location selection at road segments is predicted. 5.3.2.1 Variable selection Variables selected can be divided into four categories: pedestrian characteristics, event, traffic condition, and road g eometry. 22 variables are derived and generated to reflect their influences on pedestrian crossing choices. Table 5 2 categorically shows the selected variables in this model. Variables with indicates that this one is used as referenced variable in its c ategory. The complete dataset has 375 observations and are randomly split into the training set (80% data) for model building and test set (the other 20% data). 5.3.2.2 Model structure A time dependent sequential choice model was proposed to represent thi s behavior, as shown in Figure 5 4 Then the probability of choosing one alternative i is: (5 1 ) Where choice set ; U i is the utility function for alternative i The choice set I can be divided into two mutually exclusive subsets as I 1 and I 2 PAGE 104 104 (5 2 ) (5 3) Then we know that the probability of choosing one alternative i can be written as: (5 4 ) There are two basic post ulates for the sequential choice model ( Sheffi, 1979 ) : No alternative can be chosen without it implying that all the lower ranked alternativ es had been chosen. If an alternative is not chosen, no higher ranked alternative can be chosen. The marginal utilities of the alternatives in the choice set are independent. From these two postulates, the first term in Equation (5 4) is derived as: (5 5 ) The second term in Equation (5 4) is derived as follows (only one alternative which ranks higher than i needs to be considered): (5 6 ) Thus substituting Equation (5 5) and (5 6) into (5 4) the pro bability of pedestrian choosing to cross at location i is: (5 7 ) For simplification, we define (5 8 ) Then the model is written as: PAGE 105 105 (5 9 ) This sequential choice model is co mposed of a set of independent binary choice models. Simultaneous estimation of the binary choice models enable us to investigate trend that are related to the utilities as a function of their index set ( Sheffi, 1979 ) by maximizing the likelihood function. (5 10 ) Where S is the sample size (number of observations) and s indicates each individual. 5.3.2.3 Model speci fication and e stimation A linear form of utility is specified in this study, with the alternatives defined up to 5 crossing locations. Final model is built based on a systematic process of statistical model test and excluding the insignificant. The variabl es in the final sequential model show their statistical significance at a confidence level of 90%. The empirical variables, along with their parameters and t values are shown in Table 5 3 Coefficient of each variable reflects its impac t on crossing locati on choice. The positive sign of coefficient indicates that an increase of this variable will lead to an increase of the utility itself. On the contrary, negative coefficient has a negative effect on utility. As shown in Table 5 3, pedestrians prefer to cr oss later during an afternoon off peak. This is consistent with previous findings on driver behaviors throughout a day ( Dixit et al., 2012 ; Shinar, 1998 ) People may be more relaxed and less aggressive in making crossing decisions during afternoon off peaks than in the morning or peak period. As the increase of the pedestrian volume (along the sidewalks), the model indicates people are less likely to cross at current crosswalks and prefer to cross later. People tend to follow the moving flow if crossing at current crosswalk is not quite necessary. T he vehicular volume increase leads to less crossing at current cross walks. People prefer to cross later during high traffic condition. Higher vehicular volume decreases the pedestrian gap acceptance possibility, so pedestrians would like to postpone their crossing. PAGE 106 106 Pedestrians are more likely to cross at current crosswalks if the foreseeable delay is rather low. That said, people tend to jaywalk if encountering low waiting time at the curb. It is found that the wider the crosswalk is, the higher possibility that pedestrians would like to cross. Wide r crosswalk makes it clea r to both vehicles and pedestrians that crossings are better protected. The existence of median is negatively related to the choice of crossing location people are more likely to cross at the current crosswalk if there is a median. Median existence makes the pedestrian crossing from one stage to two stage, which directly reduces the pedestrian crossing difficulty and further increase the crossing possibility. Segment length affects the choice of crossing location. As segment length increases, people are f ound to be more willing to cross later, since they may not start to think about crossing if the destination are farther away. Based on the sequential model, pedestrian crossing probability for different crossing facilities can be estimated for primary cros sings by Equation (5 9 ). 5.3.2.4 Model prediction The model prediction results are presented in Table 5 4 (the observed share as well as the predicted share using the test data). It is shown that the predicted shares of crossing locations are very similar to the actual shares. The sequential choice model performs reasonably well as a description of pedestrian crossing choice with the variables identified. 5.3.3 Crossing Delay C rossing delay is estimated as shown in Table 5 5 according to the crossing link t ype (primary/secondary crossing). The estimation equations for signal intersections and midblock crossings are referred from Highway Capacity Manual (HCM) 2010 ( HCM, 2010 ) and the one for jaywalking is derived from Zheng and Elefteriadou ( Zheng and Elefteriadou, 2015 ) 5.3 Link Delay Estimation Link delay is defined as the delay time along the road segment due to the existence o f crossing facilities and opportunities as well as potential vehicle pedestrian interactions. A regression model considering these factors is developed to predict the pedestrian link delay. PAGE 107 107 5.3.1 Data Analysis Link delay is extracted from the pedestrian tr avel time dat a a nd is estimated as Equation (5 11 ) (5 11 ) Where is the link delay, is the total travel time provided by the GPS, is the crossing delay (wait time at intersections/crosswalks for crossing), is the link length, is the pedestrian walking speed. After examining the dataset, no serious outlier s/ influential statistics are detected ( Appendix H ). A statistical description of link delay data is provided in Table 5 6. 5.3.2 Model Development A linear regression model is developed with t he independent variables listed below. Figure 5 5 is a schematic and illustrates these variables. The statistical description of these variables is provided in Table 5 6. Pedestrian volume along the segment ( Vped ) ; Pedestrian volume on the crosswalks ( Vc p ) estimated by averaging Vc p s; Vehicle volume ( Vv eh ); Median existence ( Median ); Sidewalk width ( SW ); Segment le ngth ( L ); Vehicle Free Flow speed ( VFFS ); Pedestrian Free Flow speed ( PFFS ); Pedestrian volume per unit width ( Vp ) estimated by V ped / SW A best fitted linear regressi on model is developed by stepwise regression and the model results are shown in Table 5 7 and Table 5 8 The variables identified in the final model are all statistically significant at 95% confidence level. The pedestrian link delay is found to increase as the segment length increases. Longer segment length means a h igher exposure to pedest rian crossing facilities and vehicle interactions. PAGE 108 108 Pedestrian volume at the crosswalks has a positive impact on pedestrian link delay. By increasing the number of crossing pedestrians, the delay that the through pedestrian experience is increased, due to a dditional interference. Higher pedestrian volume or less pedestrian space at the sidewalks lead to pedestrian link delay increase, since average pedestrian encounters more interactions per unit space that may delay their movement. On average, median existe nce results in 1.14 sec of additional pedestrian link delay, keeping other variables constant. This is because median existence decreases the pedestrian critical gap, then generates more crossing possibilities, and further brings more potential vehicle int eractions. Vehicle volume is negatively associated with pedestrian link delay. Similar to median existence, lower vehicular traffic increases pedestrian crossing opportunities and further brings more vehicle interactions to pedestrian s that may delay their movement. Thus the pedestrian link delay along the road segment can be estimated by Equation (5 12) with considerations of segment length, pedestrian volume at sidewalks and crosswalks, median existence and vehicle volume. (5 1 2) Note that the assumptions for linear regression are all checked and satisfied ( Appendix H ), including residual normality, collinearity, independence, linear relationship, homogenous variance, etc. 5.4 Pedestrian Travel Time Estimation For each link al ong the pedestrian path, the travel time is estimated as the total of link walk time, link delay cross time, and crossing delay. Then, t he pedestrian total travel time at the path level is the summation of the link travel times (Equation (5 13)) (5 13) PAGE 109 109 Where is the total travel time along travel path N L is the number of links along this path, is the link delay of Link i is the crossing delay of Li nk i is the length of Link i is the pedestrian speed of Link i (based on HCM 2010) A numerical example is provided to illustrate the estimation method of pedestrian travel time along travel path (Figur e 5 6). 5.4.1 The Facts The facts of this example are provided in Table 5 9, Table 5 10, and Table 5 11 5.4.2 Solution 5.4.2.1 Link 1 Crossing Delay Link 1 is identified as a primary link (Jordan Curve). Number of crossing facilities is 5. Delay time at the signalized intersection is sec Delay time at the midblock crosswalk is PAGE 110 110 sec Delay time at jaywalking locations is sec Thus crossing delay is estimated as sec Link Delay Link Walking Time Pedestrian average walking speed is ft/s Thus link walking time is estimated as sec Link Travel Time sec 5.4.2.2 Link 2 4 Similar to Link 1, crossing delay, link delay, link walk time and total travel time for Link 2 to 4 can be estimated. Crossing Delay Link 2 (secondary crossing) 29.75 sec Link 3 (secondary crossing) 12.04 sec PAGE 111 111 Link 4 (primary crossing) 17.27 sec Link Delay Link 2 8.9 sec Link 3 14.25 sec Link 4 20.22 sec Link Walking Time Link 2 136.4 se c Link 3 170.5 sec Link 4 272.8 sec Link Travel Time Link 2 175.05 sec Link 3 196.79 sec Link 4 310.29 sec 5.4.2.3 Pedestrian Total Travel Time 5.5 Findings and Discussions An integrated method to approximate pedestrian perspective and evaluate pedestrian operations in urban networks is proposed in this study. P edestrian travel time along the path is used as the quantitative performance measure, since it represents the total time a pedestrian needs for travelling from or igin to destination, encountering different traffic conditions, and interacting with vehicles. Field data were collected in three locations through recording the real time pedestrian trajectories and speed. Based on the data, several sub models are develop ed to support the total travel time estimation. PAGE 112 112 First, crossing delay is estimated with a crossing location selection model (sequential choice). Pedestrian volume, vehicular volume, expected delay, crosswalk width, median existence and link length are iden tified as the key factors that influence pedestrian crossing choices at a particular link. Second, pedestrian link delay is estimated by a linear model to examine the relationship between pedestrian movement and crossing facilities Finally, pedestrian tra vel time along the path is obtained as the summation of each component. In general, this analytical pedestrian travel time estimation model is recommended for evaluat ing the pedestrian operations as a direct and comprehensive approach since it covers all the influencing factors as well as the mutual impact s of crossing/route alternatives along the travel path s The methodology framework and numerical example provided in this study can be followed for future applications. Future study on p edestrian route c hoices given origin and destination can be conducted and combined with the crossing location model and link delay estimation model developed in this research. PAGE 113 113 Figure 5 1. Methodological Framework PAGE 114 114 A B Figure 5 2 Data Collection Snapshots A) Data Collection App B) Data Sample in Washington, DC PAGE 115 115 Figure 5 3. Schematic of Pedestrian Primary, Secondary Crossings and Jordan Curve. PAGE 116 116 Figure 5 4. Sequential Choice Model Structure PAGE 117 117 Figure 5 5 Illustrations of Vari ables for Link Delay Estimation. PAGE 118 118 Figure 5 6. Numerical Example. PAGE 119 119 Table 5 1 Data Collection Time and Location Site Location Peak Ti me Off Peak Time Gainesville, FL University of Florida Campus Class Break Class Meeting Time Orlando, FL Orlando Downtown 11am 12pm 5pm 6pm 9am 10am 3pm 4pm Washington, D.C. D.C. Downtown 12pm 1pm 6pm 7pm 8am 9am 9am 10am PAGE 120 120 Table 5 2 Selected V ariab les for Pedestrian Crossing Choice Category Variable Type Intersection Midblock Jaywalk Response Crossing Choice Categorical Event Time Periods AM Peak Dummy # # # PM Peak Dummy # # # AM Off Peak Dummy # # # PM Off Peak Dummy # # # Weekday/Weekend Binary # # # Pedestrian Age Young Dummy # # # Adult Dummy # # # Elder* Dummy # # # Gender Binary # # # Pedestrian Volume while Crossing Numeric # # # Pedestrian Volume along Sidewalks Numeric # # # Pedestrian Speed Numeric # # # Traffic Vehicle Volume Numeric # # # Speed Limit Numeric # # # Vehicle Yield Rate Numeric N/A # # Infrastruct ure Sidewalk Width Numeric # # # Segment Length Numeric # # # Crossing Distance Numeric # # # Median Binary # # # Signal Cycle Length Numeric # N/A N/A Signal Green Time Numeric # N/A N/A Protected Pedestrian Signal Binary # N/A N/A Yield Sign Binary N/A # # Crosswalk Width Numeric # # N/A Note: indicates the variable is used as the reference variable; # indicates the variable is used for corresponding alternatives. PAGE 121 121 Table 5 3 Model Estimation Results Explanatory Variables 2|1 3|2 4|3 5|4 Est. t stat. Est. t stat. Est. t stat. Est. t stat. Constant 1.678 2.299 2.480 3.56 2.066 3. 057 1.710 2.331 AO 0.382 2.490 0.382 2.490 0.382 2.490 0.382 2.490 VEH 0.005 3.358 0.005 3.358 0.005 3.358 0.005 3.358 PED 0.002 2.198 0.002 2.198 0.002 2.198 0.002 2.198 CWW 0.166 2.469 0.166 2.469 0.166 2.469 0.166 2.469 Delay 0.169 1.604 0.169 1.604 0.169 1.604 0.169 1.604 Median 1.446 3.504 1.446 3.504 1.446 3.504 1.446 3.504 SL 0.002 4.066 0.002 4.066 0.002 4.066 0.002 4.066 Number of cases 300 Log likelihood 168.6039 Rho 2 0.2568 Adjusted Rho 2 0.2074 PAGE 122 122 Table 5 4 Sequential Model Performance. Observed Share Predicted Share (test set) 1 18.4% 16.0% 2 14.4% 14.7% 3 38.9% 34.7% 4 8.3% 14.7% 5 20.0% 20.0% Total 100.0% 100.0% PAGE 123 123 Ta ble 5 5 Crossing Delay Estimation Methods. Signal Intersections Midblock Crossings Jaywalking Estimation Equation Primary Crossing Seco ndary Crossing Note: and are the pedestrian crossing delays at signalized intersections, midblock crossings, jaywalking; an d are the pedestrian delays for primary and secondary crossings; and are the crossing probabilities at signalized intersections, midblock crossings, jayw alking; and are the number of signalized intersections, midblock crossings, jaywalking; is signal cycle length; is effective pe destrian walk time; is vehicle flow rate; is number of lanes; and are driver yield probabilities to permissible crossings and jaywalkers; is pedestrian critical gap; is average number of crossing events; is the pedestrian jaywalking probability. PAGE 124 124 Table 5 6 Statistical Description of Link Delay and Other Variables. Min. 1st Qu. Median Mean 3rd Qu. Max. Link Delay 0.1645 3.5624 6.069 5.8461 7.616 12.7926 Vehicle Volume 137 212 251 279 345 500 Ped. Volume (Sidewalk) 87 168 245 283.4 400.5 681 Segment Length 443 505 1040 805 1040 1040 Ped. V olume (Crosswalk) 90 124.1 124.1 170.4 218 446.4 Vehicle FFS 20 20 25 28.18 35 35 Pedestrian FFS 5.16 5.2 5.2 5.28 5.2 5.6 Ped. Volume per unit (Sidewalk) 0.2981 0.6143 1.26 1.6372 2.2556 4.54 Crosswalk Length 35 45 45 4 6.1 45 62 Median Existence 0 0 0 0.145 0 1 PAGE 125 125 Table 5 7 Link Delay Model Results. Estimate Std. Error t value Pr(>|t|) (Intercept) 3.960 3 0.9153 4.327 0.000 L 0.001 5 0.0003 4.316 0.000 Vcp 0.005 3 0.0004 11.975 0.000 Vp 0.3 955 0.0450 8.783 0.000 Median 1.140 5 0.4294 2.656 0.009 Vveh 0.0036 0.0016 2.187 0.031 R 2 0.4234 Adj. R 2 0.4156 Observation 375 PAGE 126 126 Table 5 8 Link Delay Model ANOVA df SS MS F Significance F Regression 5 418.5844 83.7169 5 4.1883 4.06E 42 Residual 369 570.0773 1.5449 Total 374 988.6617 PAGE 127 127 Table 5 9 Example Facts (Links). Link 1 2 3 4 Length (ft) 800 600 750 1200 Number of lanes 2 2 2 2 Effective sidewalk width (ft) 16 16 16 16 Med ian No No Yes Yes Jaywalking Yes Yes No No Jaywalker yield acceptance rate 0.8 0.8 --Pedestrian volume (ped/h) 200 240 500 650 Vehicle volume (veh/h) (bi direction) 900 800 2000 2000 Vehicle FFS (mph) 25 25 35 35 PAGE 128 128 Table 5 10 Example Facts (Intersections). Intersection 1 2 3 4 5 Type Signalized Signalized Signalized Unsignalized Signalized Cycle length (sec) 80 80 130 -122 Green time (sec) 11 11 40 -40 Signal compliance rate 0.8 0.8 0.9 -0.8 Effective crosswalk width (ft) 16 16 16 16 16 Crosswalk length with median (ft) --52 52 52 Crosswalk length without median (ft) 40 40 40 40 40 Pedestrian volume (ped/h) 200 200 500 500 500 PAGE 129 129 Table 5 11 Example Facts (Midblocks). Midblock 1 2 3 Type Marked Marked Marked Driver yield rate 0.8 0.6 0.6 Effective crosswalk width (ft) 20 25 25 Crosswalk length (ft) 40 52 52 Pedestrian volume (ped/h) 150 300 300 PAGE 130 130 CHAPTER 6 CONCLUSIONS AND RE COMMENDATIONS To advance pedestrian operational analysis to be more comprehensive in an urban network, t his dissertation develops several methodologies for evaluating and analyzing pedestrian operations with conside rations of vehicle interactions Pedestri an operational analysis in urban networks is decomposed into two levels: operational level and tactical level. Pedestrian road crossing behavior and vehicle interactions are analyzed at the operational level. Method for modeling p edestrian vehicle interact ions outside of crosswalks is first proposed and it offer s the necessary data to create and/or validate different simulation models. An improved analytical model is further developed to mathematically estimate pedestrian delay with accommodating urban netw ork characteristics. At the tactical level, p edestrian travel time estimation model along the travel path is proposed at last as an integrated approach to approximate pedestrian perspective in urban networks. 6.1 Pedestrian Vehicle Interaction Modeling P e destrian vehicle interactions outside of crosswalks (jaywalking) are commonly observed in the field especially where there are high levels of pedestrian activities. Unlike permissible crossings at crosswalks, jaywalking events are not often anticipated by drivers, which result in less driver reaction time and different vehicle operation dynamics C rossing speed, yield acceptance and delay of jaywalking crossings and permissible crossings were observed in the field and analyzed to replicat e pedestrian operat ions in simulators. B ehaviors of driver approaching jaywalkers versus pedestrians crossing at designated crosswalks are are analyzed to model the driver reactions towar ds jaywalkers. Moreover, it is found that the PAGE 131 131 environment, such as pedestrian and vehicular volume, bus stops presence and crossing distance. The se quantitative relationsh ips describing interactions between pedestrians crossing outside of crosswalks and approaching drivers are developed in this research and provide the basis and assumptions for modeling such interactions in a micro operatio nal analyses. A n improved analytical method to mathematically estimate pedestrian delay is further proposed using renewal theory with considerations of pedestrian vehicle interactions at unsignalized intersections A generalized model is first provided to accommodate different traffic flow and driver behavior assumptions. Then the proposed model is developed on the basis of a mixture of free traffic and platooned traffic with consideration of driver yielding behaviors to better replicate field conditions in an urban setting A second application using the HCM 2010 assumptions is also derived to compare it to the HCM 2010 model Lastly, f ield data were collected and used for validation from two locations: Gainesville, FL and Washington, D.C. An expanded simul ation via MATLAB is performed to evaluate the model results for a variety of cases. The comparisons to the field data as well as the simulation confirm the applicability and accuracy of the proposed model. It is also found that the current HCM 2010 model o verestimates the pedestrian delay compared with field data. 6.2 Pedestrian Travel Time Estimation For a pedestrian trip, travel route may change due to available crossing facilities, and pedestrian crossing location may affect the pedestrian overall trave l time. This dissertation evaluates each component along pedestrian travel path and proposes a model of pedestrian travel time estimation as an integrated method to approximate pedestrian perspective. Field data were collected through recording the real ti me pedestrian trajectories and speed. Based on the data, several sub models are developed to support the total travel time PAGE 132 132 estimation. First, crossing delay is estimated with a crossing location selection model (sequential choice). Pedestrian volume, vehic ular volume, expected delay, crosswalk width, median existence and link length are identified as the key factors that influence pedestrian crossing choices at a particular link. Second, pedestrian link delay is estimated by a linear model to examine the re lationship between pedestrian movement and crossing facilities Finally, pedestrian travel time along the path is obtained as the summation of each component. 6.3 Recommendations for Future Research The findings from this dissertation have implications rel ated to research, planning, and engineering solutions for future work on pedestrian safety, crosswalk design and location, as well as modeling of driver behaviors for traffic operational analyses. Research implications and recommendations for future work a re as follows. Several findings of pedestrian vehicle interactions outside of the crosswalks can be further quantified with statistical analysis: driver decision point yielding dynamics, and yield recognition behavior. The data collection procedure metho dology and result insights from this dissertation can be followed to develop larger scale studies for more generalized results. Several assumptions that used in the pedestrian delay models can be relaxed or adjusted for future research: independence of ve hicle pedestrian interactions, influencing factors of vehicle yield decision, and pedestrian gap acceptance distributions/models. Field data collection can be expanded to more sites with varying traffic conditions to validate the applicability of the propo sed generalized model. The framework of data collection for pedestrian travel time at the path level can be followed for additional data in the field. The analysis methods and results can be used to update the operational analysis of pedestrian mode and e valuate pedestrian facility performance in the HCM Pedestrian route choices given origin and destination should be explored and combined with the crossing location model and link delay estimation model developed in this research. Then a real time pedestr ian travel guidance system in urban networks can be developed with information of route selection and predicted travel time PAGE 133 133 APPENDIX A THE MEAN OF PEDESTRIAN DELAY (GENERALIZED MODEL) The expected pedestrian delays conditional on crossing in the first lag and the subsequent ordinary renewals are: (A 1) (A 2) B y unconditioning Equation (A 1) and (A 2) (A 3) thus is derived as: (A 4) is derived as: PAGE 134 134 (A 5) PAGE 135 135 APPENDIX B THE PROBABILITY DENSITY FUNCTION OF THE FIRST RENEWAL (PROPOSED MODEL) Inter arrival time (vehicle headway ) is distribute d as Cowan M3. By renewal theory, the probability distribution of the first renewal can be derived as (B 1) W here (B 2) Thus (B 3) (B 4) PAGE 136 136 APPE NDIX C THE PEDESTRIAN CROSSING PROBABILITY DENSITY FUNCTION (PROPOSED MODEL) The probability of driver yielding is a function of the time distance between the pedestrian and the vehicle itself: (C 1) It is assumed that the pedestrian yield acceptance rate is 100%, which indicates that the probability of pedestrian crossing is 100% conditional on the existence of an available gap or driver yielding. Thus the pedestrian crossing probability density function can be expressed as: (C 2) PAGE 137 137 APPENDIX D THE PROBABILITY OF ACCEPTING THE FIRST VEHICLE PEDESTRIAN LAG ( ) (PROPOSED MODEL) The probability of accepting the first vehicle pe destrian lag is: (D 1) PAGE 138 138 APPENDIX E THE PROBABILITY OF ACCEPTING THE NEXT VEHICLE PEDESTRIAN GAPS ( ) ( PROPOSED MODEL) The probability of accepting the next vehicle pedestrian gaps is: (E 1) PAGE 139 139 APPENDIX F THE MEAN OF PEDESTRIAN DELAY (PROPOSED MODEL: ) The expected pedestrian delays conditional on crossing in the first lag and the subsequent ordinary renewals are: (F 1) (F 2) By unconditioning Equation (F 1) and (F 2) (F 3) thus is derived as: (F 4) is derived as: PAGE 140 140 (F 5) Thus the expected pedestrian delay is estimated as: (F 6) Applying the probability distribution functions (B 2) and (B 4) : PAGE 141 141 (F 7) Where (F 8) (F 9) PAGE 142 142 APPENDIX G THE MEAN OF PEDESTRIAN DELAY (PROPOSED MODEL: ) Similar to Appendix F, (G 1) PAGE 143 143 APPENDIX H ASSUMPTIONS CHECK FOR LINK DELAY REGRESSION MODEL Appendix H provides the data cleanin g, processing and assumption checks for the pedestrian link delay model development. Results show that all the assumptions for linear regression are satisfied, including outlier diagnostics, residual normality, homogenous variance, independence, collineari ty, linear relationship, etc. H.1 Outliers leverage values (hat) were calculated to diagnose any influence statistics or outliers. No outliers were detected those key statisti cs of all the observations were within the reasonable intervals. H.2 Residual Normality Shapiro Francia test was conducted to check the residual normality of this model. Test statistic is 0.9877. P value is 0.2508, which concludes that the residual normal ity assumption is satisfied. H.3 Homogenous Variance Breusch Pagan test was conducted to check the variance homogeneity of this model. Test statistic is 11.2523. P value is 0.02387, which concludes that the variance homogeneity assumption is satisfied. H.4 Independent Error Over Time Durbin Watson test was conducted to check the error independence over time of this model. 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Transportation Letters Accepted for Publication. Zheng, Y., Elefteriadou, L., 2015. A Model of Pedestrian Delay at Unsignalized Intersections in Urban Networks. Transportation Res earch Part B: Methodological Under Review. Crossing Intentions in China: An Application of the Theory of Planned Behavior. Accident Analysis & Prevention 41, 491 497. China. Accident Analysis & Prevention 43, 1927 1936. PAGE 152 152 BIOGRAPHICAL SKETCH Un iversity in June 2012. After that, Yinan Zheng started her PhD program at University of engineering from University of Florida in May 2013. edestrians and traffic flow theory, with applications on travel time estimation, pedestrian crossing behaviors and vehicle pedestrian interactions in urban networks. During Yi authored four papers and made five presentations at various conferences. She won the second prize of the Southeastern Transportation Research, Innovation, Development & Education student post er Frankee Hellinger Graduate Scholarship in 2015, the User Equilibrium Award from University of Florida Transportation Institute in 2015, and the WTS Helene M. Overly Memorial Scholarship in 20 14. |