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Assessment of Car-Following Models using Field Data

Permanent Link: http://ufdc.ufl.edu/UFE0041784/00001

Material Information

Title: Assessment of Car-Following Models using Field Data
Physical Description: 1 online resource (164 p.)
Language: english
Creator: Soria, Irene
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: acceleration, aggressive, aimsun, analysis, average, calibration, car, computer, conditions, congested, conservative, corsim, data, distance, driver, error, field, following, gipps, guidelines, lead, mean, micro, mit, mitsim, model, modified, operational, optimum, parameters, pitt, rain, root, simulation, spacing, speed, square, test, traffic, trajectories, uncongested, vehicle, weather
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Computer simulation models are an important tool for analyzing and designing transportation systems. Car-following models are important components of simulation tools, since they describe the behavior of the following vehicle as a function of the lead vehicle trajectory. Over the years, several models, which estimate the following vehicle?s trajectory as a function of the speed and acceleration of the lead vehicle reaction time and spacing, have been developed. However, the literature has not reported the applicability and relative merit of various car-following models under different operational conditions such as congestion and driver type. The objective of this study is to assess car-following models using field data under different conditions. After review of existing car-following models, Gipps (component of AIMSUN simulation program), Pitt (use in CORSIM software), MITSIM (utilize in MIT simulation program), and Modified Pitt were selected. Data were obtained from a database compiled in Jacksonville, Florida. The data were collected by cameras installed in a vehicle and consist of video recordings of the speed, time and distances between the subject vehicle and its surrounding vehicles. Congested, uncongested, and rain with/without congestion were evaluated. Trajectories from subjects with different types of driving behavior (aggressive, average, and conservative) were obtained. Their field trajectories were compared to the results trajectories obtained by each of the models. An error test, Root Mean Square Error (RMSE), was used for comparing the field data and the results of the models as a key performance indicator. After initial analysis an optimum calibration was performed. The MITSIM model was found to be the best in replicating the trajectories of the drivers in all conditions. The variable best replicated by the models was speed however it is recommended to perform calibrations based on spacing. Three calibration analyses were performed: first using all the data, second using different traffic conditions, and third using each driver type. Results showed that the best results were obtained when the parameters were calibrated by driver type using MITSIM model. The study concluded with recommended calibration parameters, and application guidelines related to the car-following models examined.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Irene Soria.
Thesis: Thesis (M.E.)--University of Florida, 2010.
Local: Adviser: Elefteriadou, Ageliki L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-04-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041784:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041784/00001

Material Information

Title: Assessment of Car-Following Models using Field Data
Physical Description: 1 online resource (164 p.)
Language: english
Creator: Soria, Irene
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: acceleration, aggressive, aimsun, analysis, average, calibration, car, computer, conditions, congested, conservative, corsim, data, distance, driver, error, field, following, gipps, guidelines, lead, mean, micro, mit, mitsim, model, modified, operational, optimum, parameters, pitt, rain, root, simulation, spacing, speed, square, test, traffic, trajectories, uncongested, vehicle, weather
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Computer simulation models are an important tool for analyzing and designing transportation systems. Car-following models are important components of simulation tools, since they describe the behavior of the following vehicle as a function of the lead vehicle trajectory. Over the years, several models, which estimate the following vehicle?s trajectory as a function of the speed and acceleration of the lead vehicle reaction time and spacing, have been developed. However, the literature has not reported the applicability and relative merit of various car-following models under different operational conditions such as congestion and driver type. The objective of this study is to assess car-following models using field data under different conditions. After review of existing car-following models, Gipps (component of AIMSUN simulation program), Pitt (use in CORSIM software), MITSIM (utilize in MIT simulation program), and Modified Pitt were selected. Data were obtained from a database compiled in Jacksonville, Florida. The data were collected by cameras installed in a vehicle and consist of video recordings of the speed, time and distances between the subject vehicle and its surrounding vehicles. Congested, uncongested, and rain with/without congestion were evaluated. Trajectories from subjects with different types of driving behavior (aggressive, average, and conservative) were obtained. Their field trajectories were compared to the results trajectories obtained by each of the models. An error test, Root Mean Square Error (RMSE), was used for comparing the field data and the results of the models as a key performance indicator. After initial analysis an optimum calibration was performed. The MITSIM model was found to be the best in replicating the trajectories of the drivers in all conditions. The variable best replicated by the models was speed however it is recommended to perform calibrations based on spacing. Three calibration analyses were performed: first using all the data, second using different traffic conditions, and third using each driver type. Results showed that the best results were obtained when the parameters were calibrated by driver type using MITSIM model. The study concluded with recommended calibration parameters, and application guidelines related to the car-following models examined.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Irene Soria.
Thesis: Thesis (M.E.)--University of Florida, 2010.
Local: Adviser: Elefteriadou, Ageliki L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-04-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041784:00001


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1 ASSESSMENT OF CAR -FOLLOWING MODELS USING FIELD DATA By IRENE S. SORIA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEER ING UNIVERSITY OF FLORIDA 2010

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2 2010 Irene S. Soria

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3 To my family, loved ones and professors

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4 ACKNOWLEDGMENTS I thank my parents for always believing in me, my family for their constant support, and motivation through this journey. I th ank m y friends and my boyfriend Gabriel for being there for me motivate me and being patience. I thank m y professor s and my advisor for their guidance through this path.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...................................................................................................... 4 LIST OF TABLES ................................................................................................................ 7 LIST OF FIGURES ............................................................................................................ 14 ABSTRACT ........................................................................................................................ 16 CHAPTER 1 BACKGROUND AND OBJECTIVES ......................................................................... 18 2 LITERATURE REVIEW .............................................................................................. 20 Car -Following Models ................................................................................................. 20 Pipes and Forbes ................................................................................................. 20 General Motors (GM) ........................................................................................... 22 Newell ................................................................................................................... 24 Gazis, Herman, and Rothery (GHR) ................................................................... 25 Eddie ..................................................................................................................... 26 Kikuchi .................................................................................................................. 26 Gipps .................................................................................................................... 27 Pitt ......................................................................................................................... 29 Wiedemann and Reiter ........................................................................................ 31 Fritzsche ............................................................................................................... 36 MITSIM ................................................................................................................. 38 Modified Pitt .......................................................................................................... 40 Comparisons of Car Following Models with Field Data ............................................ 40 Literature Review Summary ....................................................................................... 44 3 METHODOLOGY ....................................................................................................... 53 Car -Following Models Literature Revi ew ................................................................... 53 Selection of the Models to be Evaluated ................................................................... 53 Implementation of the Selected Models ..................................................................... 54 Field Data Assembly ................................................................................................... 54 Data Analysis .............................................................................................................. 54 Initial Analysis ....................................................................................................... 55 Calibration Analysis ............................................................................................. 55 Performance Measurement of Each Model ........................................................ 55 Conclusions and Recommendations ......................................................................... 58

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6 4 DATA COLLECTION AND ANALYSIS PLAN ........................................................... 60 Characteristics of the Database ................................................................................. 60 Instrumented Vehicle ........................................................................................... 60 Driving Routes ...................................................................................................... 61 Description of the Database Subjects ................................................................. 61 Assembly of Data ........................................................................................................ 62 Description of In-Vehicle Data Processing .......................................................... 64 Method for Extracting Information from the Digital Cameras ............................. 64 Distances, Speed and Acceleration Calculations ............................................... 65 5 INITIAL ANALYSIS AND RESULTS COMPARISON ................................................ 74 Gipps Model ................................................................................................................ 74 Pitt Model .................................................................................................................... 79 MITSIM Model ............................................................................................................. 82 Modified Pitt Model ..................................................................................................... 86 Summary of the Initial Analysis .................................................................................. 90 6 CALIBRATION ANALYSIS ......................................................................................... 97 Parameter Calibration for Each Subject and Condition ............................................. 98 Gipps Model ......................................................................................................... 98 Pitt Model ............................................................................................................ 100 MITSIM M odel .................................................................................................... 102 Modified Pitt Model ............................................................................................. 103 Summary: Parameters Calibration for Each Model .......................................... 104 Calibration for Each Model using All Data ............................................................... 105 Calibration by Condition ........................................................................................... 106 Calibration by Driver Type ........................................................................................ 108 Summary of Findings ................................................................................................ 109 7 CONCLUSIONS AND RECOMMENDATIONS ....................................................... 142 APPENDIX A PROCEDURE USED TO OBTAINED SPEED AND LENGHT MEASUREMENTS ................................................................................................... 146 B RESULTS OF INITIAL ANALYSIS ........................................................................... 150 C PARAMETERS VALUES AFTER CALIBRATION ................................................... 155 LIST OF REFERENCES ................................................................................................. 161 BIOGRAPHICAL SKETCH .............................................................................................. 164

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7 LIST OF TABLES Table page 2-1 Parameters values for Wiedemann car -following model (Olstam and Tapani 2004) ....................................................................................................................... 46 2-2 Parameters values for Frizsche Car -following model (Olstam and Tapani 2004) ....................................................................................................................... 47 2-3 Parameters values for MITSIM car -following model (Punzo and Simonelli 2005) ....................................................................................................................... 48 2-4 Summary of car -following models ......................................................................... 49 4-1 Description of Figure 42 (Kondyli 2009) ............................................................... 68 4-2 Description of Figure 43 (Kondyli 2009) ............................................................... 69 4-3 Characteristics of instrumented vehicle experiment participants (Kondyli 2009) ....................................................................................................................... 70 4-4 Driver behavior types based on actual observations and background survey form(Kondyli 2009) ................................................................................................. 71 4-5 Trajectory of a single vehicle along with the corresponding conditions ............... 72 4-6 Second by second data for the time interval highlighted in Table 4-3 ................. 73 4-4 Inputs used in the implementation of each model ................................................. 73 5-1 Inputs used in the implementation of each model ................................................. 91 5-2 Results of the Gipps model implementation .......................................................... 91 5-3 Results of the Pitt model implementation .............................................................. 91 5-4 Results of the MITSIM model implementation ...................................................... 92 5-5 Results of the Modified Pitt model implementation ............................................... 92 6-1 G ipps car -following calibration parameters for uncongested conditions ............ 111 6-2 Gipps car -following calibration parameters for congested conditions ................ 111 6-3 Gipps car -following calibration parameters for rain uncongested conditions ..... 112 6-4 Gipps car -following calibration parameters for rain congested conditions ......... 112

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8 6-5 Calibration using all data Gipps car -following model for uncongested conditions .............................................................................................................. 117 6-6 Calibration using all data Gipps car -following model f or congested conditions .............................................................................................................. 117 6-7 Calibration using all data Gipps car -following model for rain uncongested conditions .............................................................................................................. 118 6-8 Calibra tion using all data Gipps car -following model for rain congested conditions .............................................................................................................. 118 6-9 Calibration using all data Results by driver type Gipps car -following model .. 118 6-10 Calibration using all data Total RMSE results for the Gipps car -following model .................................................................................................................... 118 6-11 Calibration using all data Pitt car -following model for unconge sted conditions .............................................................................................................. 119 6-12 Calibration using all data Pitt car -following model for congested conditions ... 119 6-13 Calibration using all data Pitt car -following model for rain uncongested conditions .............................................................................................................. 119 6-14 Calibration using all data Pitt car -following model for rain congested conditions .............................................................................................................. 120 6-15 Calibration using all data Results by driver type Pitt car -following model ....... 120 6-16 Calibration using all data Total RMSE results for the Pitt car -following m odel .................................................................................................................... 120 6-17 Calibration using all data MITSIM car -following model for uncongested conditions .............................................................................................................. 121 6-18 Calibration using all data MITSIM car -following model for congested conditions .............................................................................................................. 121 6-19 Calibration using all data MITSIM car -following model for rain uncongested conditions .............................................................................................................. 122 6-20 Calibration using all data MITSIM car -following model for rain congested conditions .............................................................................................................. 122 6-21 Calibration using all data Results by driver type MITSIM car -following mo del .................................................................................................................... 123

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9 6-22 Calibration using all data Total RMSE results for the MITSIM car -following model .................................................................................................................... 123 6-23 Calibration using all data Modified Pitt car -following model for uncongested conditions .............................................................................................................. 123 6-24 Calibration using all data Modified Pitt car -following model for congested conditions .............................................................................................................. 124 6-25 Calibration using all data Modified Pitt car -following model for rain uncongested conditions ....................................................................................... 124 6-26 Calibration using all data Modified Pitt car -following m odel for rain congested conditions ........................................................................................... 124 6-27 Calibration using all data Results by driver type Modified Pitt car -following model .................................................................................................................... 125 6-28 Calibration using all data Total RMSE results for the Modified Pitt car following model ..................................................................................................... 125 6-29 Calibration by condition Gipps car -following model for uncongested conditions .............................................................................................................. 126 6-30 Calibration by condition Gipps car -following model for congested conditions 126 6-31 Calibration by condition Gipps car -following mo del for rain uncongested conditions .............................................................................................................. 126 6-32 Calibration by condition Gipps car -following model for rain congested conditions .............................................................................................................. 127 6-33 Calibration by condition Results by driver type Gipps car -following model .... 127 6-34 Calibration by condition Total RMSE results for the Gipps car -following model .................................................................................................................... 127 6-35 Calibration by condition Pitt car -following model for uncongested conditions 128 6-36 Calibration by condition Pitt car -following model for congested conditions .... 128 6-37 Calibration by condition Pitt car -following model for rain uncongested conditions .............................................................................................................. 128 6-38 Calibration by cond ition Pitt car -following model for rain congested conditions .............................................................................................................. 129 6-39 Calibration by condition Results by driver type Pitt car -following model ......... 129

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10 6-40 Calibration by condition Total RMSE results for the Pitt car-following model 129 6-41 Calibration by condition MITSIM car -following model for uncongested conditions .............................................................................................................. 130 6-42 Calibration by condition MITSIM car -following model for congested conditions .............................................................................................................. 130 6-43 Calibration by condition MITSIM car -fol lowing model for rain uncongested conditions .............................................................................................................. 131 6-44 Calibration by condition MITSIM car -following model for rain congested conditions .............................................................................................................. 131 6-45 Calibration by condition Results by driver type MITSIM car -following model 132 6-46 Calibration by condition Total RMSE results for the MITSIM car -following model .................................................................................................................... 132 6-47 Calibration by condition Modified Pitt car -following model for uncongested conditions .............................................................................................................. 132 6-48 Calibration by condition Modified Pitt ca r-following model for congested conditions .............................................................................................................. 132 6-49 Calibration by condition Modified Pitt car -following model for rain uncongested conditions ....................................................................................... 133 6-50 Calibration by condition Modified Pitt car -following model for rain congested conditions .............................................................................................................. 133 6-51 Calibration by condition Results by driver type Modified Pitt car -following model .................................................................................................................... 133 6-52 Calibration by condition Total RMSE results for the Modified Pitt car following model ..................................................................................................... 133 6-53 Calibration by driv er type Gipps car -following model for uncongested conditions .............................................................................................................. 134 6-54 Calibration by driver type Gipps car -following model for congested conditions .............................................................................................................. 134 6-55 Calibration by driver type Gipps car -following model for rain uncongested conditions .............................................................................................................. 135 6-56 Calibration by driver type Gipps car -following model for rain congeste d conditions .............................................................................................................. 135

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11 6-57 Calibration by driver type Results by driver type Gipps car -following model .. 135 6-58 Calibration by driver typ e Total RMSE results for the Gipps car -following model .................................................................................................................... 1 35 6-59 Calibration by driver type Pitt car -following model for uncongested conditions .............................................................................................................. 136 6-60 Calibration by driver type Pitt car -following model for congested conditions .. 136 6-61 Calibration by driver type Pitt car -following model for rain uncongested conditions .............................................................................................................. 136 6-62 Calibration by driver type Pitt car -following model for rain congested conditions .............................................................................................................. 137 6-63 Calibration by driver type Re sults by driver type Pitt car -following model ...... 137 6-64 Calibration by driver type Total RMSE results for the Pitt car -following model .................................................................................................................... 137 6-65 Calibration by driver type MITSIM car -following model for uncongested conditions .............................................................................................................. 138 6-66 Calibration by driver type MITSIM car -following model for congested conditions .............................................................................................................. 138 6-67 Calibration by driver type MITSIM car -following model for rain uncongested conditions .............................................................................................................. 139 6-68 Calibration by driver type MITSIM car -following model for rain congested conditions .............................................................................................................. 139 6-69 Calibration by driver type Results by driver type MITSIM car -following model .................................................................................................................... 140 6-70 Calibration by driver type Total RMSE results for the MITSIM car -following model .................................................................................................................... 140 6-71 Calibration by driver type Modified Pitt car -following model for uncongested conditions .............................................................................................................. 140 6-72 Calibration by driver type Modified Pitt car -following model for congested conditions .............................................................................................................. 140 6-73 Calibration by driver type Mo dified Pitt car -following model for rain uncongested conditions ....................................................................................... 141

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12 6-74 Calibration by driver type Modified Pitt car -following model for rain congested conditions ........................................................................................... 141 6-75 Calibration by driver type Results by driver type Modified Pitt car -following model .................................................................................................................... 141 6-76 Calibration by driver type Total RMSE results for the Mod ified Pitt car following model ..................................................................................................... 141 B-1 Gipps results for each driver in uncongested and congested conditions ........... 150 B-2 Gipps results for each driver in rainy uncongested and congested conditions .. 151 B-3 Pitt results for each driver in uncongested and congested conditions ............... 151 B-4 Pitt results for each driver in rainy uncongested and congested conditions ...... 152 B-5 MITSIM results for each driver in uncongested and congested conditions ....... 152 B-6 MITSIM results for each driver in rainy uncongested and congested conditions .............................................................................................................. 153 B-7 Modified Pitt results for each driver in uncongested and congested condi tions 153 B-8 Modified Pitt results for each driver in rainy uncongested and congested conditions .............................................................................................................. 154 C-1 Pitt car -following calibration parameters for uncongested conditions ................ 155 C-2 Pitt car -following calibration parameters for congested conditions .................... 155 C-3 Pitt car -f ollowing calibration parameters for rain uncongested conditions ......... 156 C-4 Pitt car -following calibration parameters for rain congested conditions ............. 156 C-5 MITSIM car -following calibration parameters for uncongested conditions ........ 157 C-6 MITSIM car -following calibration parameters for congested conditions ............. 157 C-7 MITSIM car -following calibration parameters for rain uncongested conditions 158 C-8 MITSIM car -following calibration parameters for rain congested conditions ..... 158 C-9 Modified Pitt car -following calibration parameters for uncongested conditions 159 C-10 Modified Pitt car -following calibration parameters for congested conditions ..... 159

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13 C-11 Modified Pitt car -following calibration parameters for rain uncongested conditions .............................................................................................................. 160 C-12 Modified Pitt car -following calibration parameters for rain congested conditions .............................................................................................................. 160

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14 LIST OF FIGURES Figure page 2-1 Different thresholds and regimes in the Wiedemann car -following model (VISSIM 5.10 User guide) ...................................................................................... 46 2-2 Phase diagram presenting the five different modes of Fritzsche car -following model (Fritzsche 1994) .......................................................................................... 47 3-1 Flowchart of the methodology ................................................................................ 59 4-1 Inside view of the TRC instrumented vehicle ........................................................ 67 4-2 AM route (Kondyli 2009) ........................................................................................ 68 4-3 PM route (Kondyli 2009) ........................................................................................ 69 4-4 Image geometry with A) Horizontal camera axis and B) Measurements on the digital image.(Psarianos et al., 2001) .................................................................... 72 5-1 Spacing between lead and follower vehicle for each time interval (uncongested condition, subject 67) ...................................................................... 93 5-2 Follower vehicle speed for each time interval (uncongested condition, subject 67) ........................................................................................................................... 93 5-3 Spacing between lead and follower vehicle for each time interval (congested condition, subject 67) ............................................................................................. 94 5-4 Follower vehicle speed for each time interval (congested condition, subject 67) ........................................................................................................................... 94 5-5 Spacing between lead and follower vehicle for each time interval (rain uncongested condition, subject 67) ....................................................................... 95 5-6 Follower vehicle speed for each time interval (rain uncongested condition, subject 67) .............................................................................................................. 95 5-7 Spacing between lead and follower vehicle for each time interval (rain congested condition, subject 67) ........................................................................... 96 5-8 Follower vehicle speed for each time interval (rain congested condition, subject 67) .............................................................................................................. 96 6-9 After spacing calibration Spacing between lead and follower vehicle for each time interval (unco ngested condition, subject 67) ...................................... 113

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15 6-10 After spacing calibration Follower vehicle speed for each time interval (uncongested condition, subject 67) .................................................................... 113 6-11 After spacing calibration Spacing between lead and follower vehicle for each time interval (congested condition, subject 67) .......................................... 114 6-12 After spacing calibration Follow er vehicle speed for each time interval (congested condition, subject 67) ........................................................................ 114 6-13 After spacing calibration Spacing between lead and follower vehicle for each time interval (rain uncongested condition, subject 67) ............................... 115 6-14 After spacing calibration Follower vehicle speed for each time interval (rain uncongested condition, subject 67) ..................................................................... 115 6-15 After spacing calibration Spacing between lead and follower vehicle for each time interval (rain congested condition, subject 67) ................................... 116 6-16 After spacing calibration Follower vehicle speed for each time interval (rain congested condition, subject 67) ......................................................................... 116 A-1 Image acquisition geometry with camera axis horizontal (left) and tilted (right) (Psarianos et al. 2001) ......................................................................................... 146 A-2 Graphical determination of vanishing points ....................................................... 147 A-3 Measurements on the digital camera Psarianos et all (2001) ............................ 148 A-4 Images of the process for estimating the 0 and .......................................... 148

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16 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering ASSESMENT OF CAR-FOLLOW ING MODELS USING FIELD DATA By Irene S Soria May 2010 Chair: Lily Elefteriadou Major: Civil Engineering Computer simulation models are an important tool for analyzing and designing transportation systems. Car -following models are important components of simulation tools, since they describe the behavior of the following vehicle as a function of the lead vehicle trajectory. Over the years, several models, which estimate the following vehicles trajectory as a function of the speed and acceleration of the lead vehicle reaction time and spacing, have been developed. However, the literature has not reported the applicability and relative merit of various car -following models under different operational conditions such as congestion and driver type. The object ive of this study is to assess car -following models using field data under different conditions. After review of existing car -following models, Gipps ( component of AIMSUN simulation program ), P itt (use in CORSIM software ), MITSIM ( utilize in MIT simulation program), and Modified P itt were selected. Data were obtained from a database compiled in Jacksonville, Florida. The data were collected by cameras installed in a vehicle and consist of video recordings of the speed, time and distances between the subject vehicle and its surrounding vehicles Congested, uncongested, and rain with/ without congestion were evaluated.

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17 Trajectories from subjects with different type s of driving behavior (aggressive, average, and conservative) were obtained. Their field trajectories were compared to the results trajectories obtained by each of the models. An error test, Root Mean Square Error (RMSE), was used for comparing the field data and the results of the models as a key performance indicator. After initial analysis an optimu m calibration was performed The MITSIM model was found to be the best in replicating the traj ectories of the drivers in all conditions. T he variable best replicated by the models was speed however it is recommended to perform calibrat ions based on spacing Three c alibration analyses were performed : first using all the data, second using different traffic conditions and third using each driver type. Results showed that the best results were obtained when the parameters were calibrated by driver type using MITSIM model The study concluded with recommended calibration parameters, and application guidelines related to the car -following models examined.

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18 CHAPTER 1 BACKGROUND AND OBJEC TIVES Computer simulation programs have been playing an important role in th e design and analysis of transportation systems. Simulation modeling applications and tools are being applied by transportation professionals and traffic engineers to address problems related to the design and operations of highways. Today, these professionals use microscopic simulation programs to replicate different highways environments and evaluate different alternatives solutions. These micro -simulation programs have been developed worldwide and their algorithms, characteristics and properties have been based on different algorithms of microscopic driver behavior These algorithms include lane changing, gap acceptance and car -following Car -following models describe the behavior of the following vehicle as a function of the lead vehicle trajectory. Kno wing the lead vehicle trajectory and using the car following models one can be estimate or predict the following vehicle trajectory in response to the lead vehicles actions. Existing car -following models typically consider the speed of the lead and follow ing vehicles, and the acceleration of the lead vehicle. Some models consider the reaction time of the following vehicle, as well as the spacing, and relative speed. However, existing literature has not reported on the applicability and relative merit of various car -following m odels under different operational conditions (congested vs. non-congested), and for different types of drivers. The purpose of this thesis is to asses sel ected car -following models and their performance against field data under differe nt conditions (congested, uncongested and rain with/without congestion), and for different drivers types (conservative, average and

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19 aggressive) Such comparison would result in a better understanding of the models and their capabilities. More specifically the objectives of this study are to : 1. Calculate the projected trajectories for selected car -following models under different traffic conditions and compare the model estimated trajectories with those obtained in the field. 2. Compare the following: a. Trajectories obtained by the selected models b. Trajectories obtained under different traffic conditions (congested vs. uncongested, and rain vs. no rain) c. Trajectories obtained among different drivers 3. Provide recommendations regarding improvements to existing car -following models and their application. Chapter 2 present s a literature review of different car -following models and a discussion of the car -following models selected. In addition it includes previous studies performed comparing field data with car -following mod els. Chapter 3 describes the methodology used in this study. Chapter 4 explains the field data used and the process of assembling it for this study. Chapter 5 includes an initial analysis of the models using the field data and default values of the paramet ers for each selected model, while Chapter 6 summarizes the calibration analysis. Lastly conclusions and recommendations are presented in Chapter 7.

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20 CHAPTER 2 LITERATURE REVIEW The chapter summarizes past research related to the development and evaluatio n of car -following models. This chapter will be divided in three sections. First will be a review of car -following models while the second subsection will summariz e previous research that has been conducted comparing car -following models with field data. T he chapter concludes with a summary of the literature findings and recommendations for future research. Car -Following Models The literature of car -following theory is extensive and it has been developed since the 1950s. This thesis discusses some of the mo re prevalent car -following models. Pipes and Forbes The pioneers of this theory were Pipes and Reuschel in early 1950s (May 1990) May (1990) ex plained that Pipes characterized the motion of the vehicles in the traffic stream as following rules suggested in the California Motor Vehicle Code. According to Pipes car -following theory, the minimum safe distance headway increase linearly with speed and the safe time headway continuously decrease with speed and theoretically reach absolute minimum time headway of 1.36 seconds at a speed of infinity (May 1990) Pipes assumed that the movements of the various vehicles of the line obey a following rule suggested by a rule of thumb frequently taught in driver training, which is to allow one additional length of a car in front for ever y ten mi per hour of speed. Equation 21 presents Pipes car -following model. +1= + +1+ (2-1) Where:

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21 is the position of the front of the nth vehicle, +1 is the position of the front of the (n+1)th vehi cle, is the minimum distance bet ween the vehicles when stopped, is the time gap, +1 is the velocity of the (n+1)th vehi cle is the length of the nth vehicle. If the Equation 2-1 is differentiated E quation 2-2 will be obtained representing the speed differential. +1= +1 (2-2) Where: is the velocity of the nth vehicle, +1 is the velocity of the (n+1)th vehicle, is the time gap, +1 is the accelera tion of the (n+1)th ve hicle May ( 1990 ) observed that speed increases the minimum distance headway increase and the time headway decreases. In lower speed situations almost every vehicle is in car -following mode and the distance headway is at minimum so there time headway decreases. On the other hand in higher speed situations all the vehicles are not traveling at the same speed and the distance headway between pairs of vehicles varie s widely Observing Equation 2-1 the spacing between vehicles is a function of the velocity of the follower, the length of the vehicle and the minimum distance that the follower accepts. This equation does not take into consideration the breaking of the lead vehicle in emergenc y situ ations and the velocity of the follower R eaction time and driver behavior are also not considered in this formula. Forbes approached car -following behavior by taking into consideration the reaction time needed for the following vehicle to perceive the need to decelerate and apply the

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22 brakes (May 1990) This is the time gap between the vehicles and this distance should always be equal or greater than the reaction time. Therefore the time headway is equal to the reaction time and the time for the lead vehicle to traverse a distance equivalent to its length. Th is model is similar of Pipes model so it can be used for lower speed but for higher speeds the pattern changes. Pipes and Forbes dont consider the acceleration, desired speed of the drivers and the dynamic elements of the following vehicle. They are stati c models which are useful as simplifying assumptions but they dont consider driver behavior or traffic conditions in detail General Motors ( GM ) A simple linear model was proposed by Ch andler et al. (1958) with the assumption that the response (acceleration or deceleration) of the following vehicle is proportional to the stimuli (relative velocity) between the lead and following vehicles. According to this model a driver accelerates (or decelerates) in response to the velocity changes of the lead vehicle. They propose d an equation that response = F (sensitivity, stimuli), developing a stimulus -response car -following concept. They suggested that drivers apply acceleration or deceleration in proportion to the speed difference between the lead and following vehicles. They developed a linear model with the assumption that the driver of the following vehicle controls the accelerator (or brake) to keep zero relative speed to the leading vehicle (Ahn et al. 2004) The General Motors research team develop ed five generations of car -following models, all of which took the form of Response = Sensitivity Stimuli. GM researcher used test tracks and tunnels field data. This data was collected using a cable and reel apparatus attached to the bumpers of the lead and traveling veh icles. T hey d id nt

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23 include open roadway data. Herman et al. (1959) explained that a sensitivity parameter was used in the equation to account the differences in the level of response observed for various drivers under different distance headway s and traffic stream speed conditions The model included four special case equations and a single general case equation known as the GM fifth model (Herman et al. 1959) Equat ion 2 3 represents the GM fifth model. +1( + ) = [ +1( + ) ][ ( ) +1( ) ] [ ( ) +1( ) ] (2-3) Where: is the velocity of the nth vehicle, +1 is the velocity of the (n+1)th vehicle, +1 is the acceleration of the (n+1)th vehicle, is the reaction time, is a sensitivity parameter, and are constants to be calibrated. The GM experiments included the estimation of a characteristic speed using the sensitivity factors and average distance headway values (Herman et al. 1959) Also the GM research used position, speed and acceleration parameters of two vehicle platoons to esti mate driver behavior responses. T he field data revealed significant variation in the sensitivity values across different drivers; h owever, the model could not accommodate or explain this variation. R esearchers explained that this increase of the sensitivity pa rameter is associated to the relative spacing decreases. The General Motors car -following models do not consider the effect of the inter vehicle spacing independently of the relative velocity; for example drivers will always accelerate if the relative velo city is positive and decelerate if the relative velocity is negative. On the other hand, in real driving, it is often seen that

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24 when the following vehicle is some reasonable distance behind the leading vehicle, the following vehicle can accelerate even if the relative velocity is zero. This model doesnt recognize the preferred speeds or the desire of the following vehicle to drive. Newell Zhang and Kim (2005) describe the Newell (1961) car -following model as follows: ( + ) = [1 ( 1( ) ( ) )] (2-4) Where: is the velocity of the nth vehicle, is the position of the front of the nth vehicle, 1 is the position of the front of the (n 1)th vehi cle, is the length of the vehicle, is the free flow speed, is the slope of the spacing This model states that if the lead vehicle travels at a constant velocity the following vehicle will follow at the same velocity assum ing that the velocity of the following vehicle is not its desirable velocity. The model assumes that since vehicles are traveling on a homogeneous road segment, the spacing of the vehicles will remain the same as long as the velocity of the lead vehicle is constant and hasnt changed. However if the lead vehicle alters its velocity and then remains at this new velocity for some time, the trajectory of the follower can be approximated by linear extrapolations. This model follows that each driver adopts her own relation between velocity and spac ing and this relation is linear. Newell transformed his car -following model into macroscopic one to describe the average driver behavior and this transformation lead to a linear relation be tween queued flow and densities (Ahn et al. 2004)

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25 Gazis, Herman, and Rothery (GHR) Gazis et al. (1961) developed a nonlinear car -following model with a sensitivity term that was inversely proportional to the relative spacing. They suggested that the previous car -following models should be modified by adding the psychological factors shown by the Response = Sensitivity Stimuli model. They recommended adding the response of the driver the sensitivi ty term, and stimuli. They proposed a cross correlation method to estimate the reacti on time. The time lag that produces the highest correlation between relative speed and acceleration of the following vehicle was identified as the reaction time. Initially, the GHR model only controls the actual following behavior. The basic relationship between the leader and the follower vehicle is in this case a stimulus response action type of function. The GHR model states that the followers acceleration is proportional to the speed of the follower, the speed difference between the follower and the le ader, and the space headway. Brackstone and McDonald (1999) present the GHR car -following model as follows : ( ) = ( ) ( ) ( ) (2-5) Where: is the acceleration of vehicle n at time t, the speed of the nth vehicle, and the relative spacing and speeds, respectively between the nth and n + 1 vehicle (the vehicle immediately in front ), is the driver reaction time, and are the constants

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26 Observing E quation 2-5 it can be concluded that if the relative speed between vehicles is zero the reaction time variable is going to disappear; in reality the driver reaction time will always be present no matter the conditions of the traffic. Eddie Edie (1961) developed an addit ional car -following model He assumed that as the speed of the traffic stream increases, the driver of the following vehicle would be more sensitive to the relative velocity between the lead and following vehicles. Therefore, he introduced the speed of the following vehicle into the sensitivity term of the nonlinear model developed by Gazis et al. (1959) Fin ally, a generalized form of car -following models was proposed Gazis et al. (1961) that allowed various modification of the sensitivity term. Edie (1961) Newell (1961) and Gazis e et al. ( 1959) studied nonlinear car following models considering the human factors, and stated that although it is difficult to find a reliable nonlinear model which can represent real following conditions, only a nonlinear model can reflect real car -following si tuations. Kikuchi Chakroborty and Kikuchi (1999) recognized that the reactions of the following vehicle to the lead vehicle might not be based on a deterministic relationship, but rather on a set of approximate driving rules developed through experience. Their approach to modeling these rules consisted of a fuzzy inference system with relationship sets that could be used to describe and quantify the behavior of following vehicles. However, the logic to define the relationship sets is subjective and depends totally on the judgment and approximation of the researchers. No field experiments were conducted to calibrate and validate these fuzzy relationship sets under real driving conditions.

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27 Gipps This model takes into consideration the desired speed of the following vehicle, the breaking mode and the car -following mode. Gipps model is recognized as a multi regime model. It calculate s two speeds : one is the desired speed and the other the speed that will be cons trained by the vehicle in front. The minimum of th ese two speed s is selected to estimate the follower vehicle speed. The equation of car -following is based on the max imum safety deceleration and the distance between vehicles. Gipps (1981) claimed that the parameters and in the general ized form of General Motors car -following models have no connection with identifiable characteristics of drivers or vehicles, and argued that the parameters in a model should correspond to obvious characteristics of drivers and vehicles. Therefore, he proposed a model for the response of the following vehicle based on the assumption that each driver sets limits to his desired braking and acceleration rates, and then uses these limits to calculate a safe speed with respect to the preceding vehicle. It was assum ed that the driver of the following vehicle selects his speed to ensure that he can bring his vehicle to a safe stop if the vehicle ahead comes to a sudden stop. Gipps car -following model is represented as follows : ( + ) = min ( ) +2.5 1 ( ) 0. 025 +( ) 1 2 + 22[2 [ 1( ) 1( )] ( ) 1( )2 ]) } (2-6) Where: is the maximum acceleration which the driver of vehicle n wishes to undertake

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28 is the actual most severe deceleration rate that the driver of vehicle n wishes to undertake ( < 0) is the estimated most severe deceleration rate that the vehicle n-1 is willing to employ, 1 is the effective size of vehicle n; that is the physical length plus a margin into which the following vehicle is not willi ng to intrude even when at rest, 1 is the speed at w hich the driver of vehicle n-1 wishes to travel, is the speed at which the driver of vehicle n wishes to travel ( ) is the location of the front of vehicle n at time t 1( ) is the location of the front of vehicle n at time t is the speed at which the driver of vehicle n wishes to travel is the apparent reaction time, a constant for all vehicles. The second term in the equation represent that congested conditions exists and/or vehicles are traveling as fast as the volume of vehicles permit. The first term represent the vehicles traveling freely. The speed of the follower according to Gipps is defined by the minimum of these two equations. Gipps emphasizes that the only applications of the model in which a smooth transition does not necessarily occur are when the leading vehicle brakes harder than the following vehicle has anticipated or leaves the lane or when a new vehicle moves into the gap between two vehicles. However, these are the circumstances under which real traffic may also exhibit a rapid transition between acceleration and braking (Gipps 1981) If the lead vehicle brakes unexpected or react to changes in the network Gipps equation will not calculate this threshold. It can be assumed that if the follower speed calculated is the minimum in the equation based of the lead trajectory the network is congested or the distance between vehicles is small.

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29 Gipps claims that the model proposed appears to be able to mim ic the behavior of real traffic. He discussed that the parameters involved correspond to obvious driver and vehicle characteristics and affect the behavior of the simulated flow in l ogically consistent ways. An advantage of the model is its speed calculations the equation contains square roots and squares but not general powers of variables, so it is relatively fast to evaluate. A critique of this model is that it assumes a constant reaction time for all the drivers in all the situations, considers that the driver is homogeneous and it is difficult to include in the equation different network characteristics. Pitt Pitt model is considered as a stimulus response model The basic assumption is that the following vehicle will maintain a given space headway. This model is similar to the concept of the GM mode calculating the distances between vehicles but adding different constant of calibrations. The Pitt car -following m odel Equation 27, describe s that the follower vehicle will try to maintain minimum space headway equal to 5N5N 5N5N = + 3. 04878 + + 5O5O ( )2 (2-7) Where: 5N5N = space headway between the lead vehicle B and the follower A fr om front bumper to front bumper = lead vehicle (B) length, = the car -following parameter (sensitivity factor), & = speed of vehicles lead and follower respectively = calibration constant defined as 0.1(wh en > ) or 0 otherwise.

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30 For the car -following parameter (sensitivity factor) CORSIM utilize s values from 1.25 for the timid drivers to 0.35 for the aggressive drivers. El Khoury and Hobeika (2006) proposed a range of 1.6 for timid drivers and 0.3 for aggressive drivers. For the length of the vehicle an average vehicle length of 7.62 m (25ft) was used. This model set a desired amount of headway for individual drivers. Vehicles seek to maintain a minimum car -following distance while not exceeding their maximum speed. Each of the drivers in this model has a unique, desired headway. If the current distance is not sufficient to maintain the desired headway, the vehicle will decelerate in an effort to attain the desired headway. If the distance s are larger than the desired headway the vehicle will attempt to accelerate to achieve the desired headway unless it is at its desired free-flow speed. The behavior of a lead vehicle is also dependent on the upcoming network characteristics (e.g., changes in lane configuration, turning movemen ts, control, blockages, etc.). The vehicle will scan the upcoming network objects and attempt to adjust its speed or lane in order to react to the objects. The simulation program CORSIM (CORridor SIMulation) utilizes the Pitt car following model. This program was developed by the US Federal Highway Administration (FHWA) for simulatio n of traffic behavior on integrated urban transportation networks of freeway and surface streets. CORSIM combines the NETwork SIMulation (NETSIM) and FREeway SIMulation (FRESIM) models into an integrated package. Both NETSIM and FRESIM simulate traffic beh avior at a microscopic level with detailed representation of individual vehicles and their interaction

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31 with their physical environment and other vehicles. The FRESIM model utilizes the Pitt car -following model of Equation 2-7 while NETSIM uses the car -foll owing model in Equation 28. = + + + 5F5F (2-8) Where: = distance traveled by follower vehicle over time interval = distance traveled by follower vehicle during its reaction time, = distance required by follower vehicle to come to a complete stop, 5F5F = distance required by lead vehicle to come to a complete stop. Wiedemann and Reiter Wiedemann and Reiter car -following model uses thresholds or actions points where the driver changes his/her behavior. This model is known as psycho ph ysical model. Figure 2-1 displays the thresholds and regimes of Wiedemmann model. These thresholds can be categorized in four driving modes: 1. Free driving: no influence of leading vehicles. In this mode the follower vehicle seeks to reach and maintain her/ h is indivi dually desired speed. 2. Approaching: when passing the approaching point ( SDV) threshold. T he process of adapting the drivers own speed to the lower speed of the lead vehicle. While approaching, a driver applies a deceleration so that the speed diff erence of the two vehicles is zero in the moment she/ he reaches her/ his desired safety distance. Wiedemann and Reiter (1992) include another threshold similar to SDV; CLDV, decreasing speed difference. This threshold is used to model perception of small speed difference at short, decreasing distances. In VISSSIM this threshold is ignored and CLDV is assumed to be equal t o SDV 3. Following: the thresholds SDV, ABX ( desired minimum following distance at low speed differences ), SDX (the maximum following distance ), and OPDV (the increasing speed difference) constitutes the following regime. The driver follows the preceding car without any conscious acceleration or deceleration. She/ he keeps the safety distance more or less constant. 4. Braking or emergency regime : when the front to rear distance is smaller than ABX the follower adopted the emergency regime. The application of medi um to high deceleration rates if the distance falls below the desired safety distance.

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32 This can happen if the preceding car changes speed abruptly, of if a third car changes lanes in front of the observed driver. For each mode, the acceleration is described as a result of speed, speed difference, distance and the individual characteristics of driver and vehicle. The driver switches from one mode to another as soon as she/ he reaches a certain threshold that can be expressed as a combination of speed difference and distance. For example, a small speed difference can only be realized in small distances, whereas large speed differences force approaching drivers to react much earlier. The ability to perceive speed differences and to estimate distances varies among the driver population, as well as the desired speeds and safety distances. Because of the combination of psychological aspects and physiological restrictions of the drivers perception, the model is called a psych o-physical car -following model. As notice d each threshold contained calibration parameters. Figure 2 -2 provides the assumed calibration parameters that Olstam and Tapani utilized for their research p aper. These parameters were based on the parameters used by the VISSIM simulation program. However, there is not clear in the manual and in the references how the values of these parameters were calculated or the explanation for assuming this numbers. Th e Wiedemann car -following model is utilized in the simulation program VISSIM. In VISSIM the following car -following models available are : Wiedemann 74: Model mainly appropriate for urban traffic Wiedemann 99: Model mainly suitable for interurban (motorway) traffic No Interaction: Vehicles do not recognize any other vehicles (can be used for a simplified pedestrian behavior).

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33 Wiedemann 74 is based on the concept that the driver of a faster moving vehicle starts to decelerate as s he/ he reaches her/ his individual perception threshold to a slower moving vehicle. Since she/ he cannot exactly determine the speed of that vehicle, her/ his speed will fall below that vehicles speed until she/ he starts to slightly accelerate again after reaching another perception threshold. This results in an iterative process of acceleration and deceleration. (VISSIM 5.10 manual). For Wiedemann 74 the safety distance can be calculated as follows: = 5454 + 5555 (29) Where: 5454 i s the average standstill distance that defines the average desired distance between stopped cars. I t has a fixed variation of 1m, 5555 is c alculated in Equation 2 -10. 5555 = ( 5555 5N5N5N5N + 5555 5Z5Z5Z5Z5Z5Z ) (210) Where: 5555 5N5N5N5N i s the additive part of desired safety distance, 5555 5Z5Z5Z5Z5Z5Z i s the multiplic part of the desired safety distance that affects the computation of the safety distance is the vehicle speed [m/s] is a value of range [0,1] which is normal distributed around 0.5 with a standard deviation of 0.15 Wiedemann 99 is based in 13 parameters and the safety dis tance is calculated as follows: 5Q5Q 5`5`5`5`5`5`5`5` = 0 + 1 (211) Where: 0 is the standstill distance,

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34 1 is the time headway, the time ( s) that a driver wants to keep. The higher the value, the more cautious the driver is is the vehicle speed. There are parameters available in VISSIM based on driver behavior and reaction time; However it is not clear in the manual and in any referenced documents how these parameters affect car -following equation. These parameters are defined as follows: 2 (Following variation) restricts the longitudinal oscillation or how much more distance than the desi red safety distance a driver allows before she/ he intentionally moves closer to the car in front. If this value is set to e.g. 10 m, the following process results in distances between 5Q5Q 5`5`5`5`5`5`5`5` an d 5Q5Q 5`5`5`5`5`5`5`5` + 1 0 The default value is 4.0 m which results in a quite stable following process. 3 (Threshold for entering Following) controls the start of the deceleration process when a driver recognizes a preceding slower vehicle. In other words, it defines how many seconds before reaching the saf ety distance the driver starts to decelerate. 3 is a negative number, and controls the time before reaching the safety distance that a driver begins to decelerate. This value does not represent the rate at which the driver decelerates and therefore on Lownes and Machemehl results this parameter has a slight impact on roadway capacity. 4 and 5 (Following thresholds) control the speed differences during the f ollowing state. Smaller values result in a more sensitive reaction of drivers to accelerations or decelerations of the preceding car, for example the vehicles are more tightly coupled. 4 is used for negative and 5 is positive speed differences. The default values result in a fairly tight restriction of the following process.

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35 6 (Speed dependency of oscillation): Influence of distance on speed oscillation while in following process. If set to 0 the speed oscillation is independent of the distance to the preceding vehicle. Larger values lead to a greater speed oscillation with increa sing distance. 7 (Oscillation acceleration): Actual acceleration during the oscillation process. 8 (Standstill acceleration): Desired acceleration when starting from standstill (limited by maximum acceleration defined within the acceleration curves) 9 (Accele ration at 80 km/h (50 mi /hr )) is a car -following parameter that affect the acceleration behavior of the following vehicles when they are traveling at 50 mi /hr (80.5 km/h). Equation 2-11 depends on the parameter of stopped condition distance 0 that repr esents the distance that the driver wishes to maintain behind a stopped vehicle on the freeway. The value of this parameter affects in the capacity of a network. Lownes and Machemehl (2006) discovered that high values of 0 reduced the capacity on VISSIM. Lowering this value the capacity of the network increased. This result is reasonable because if the vehicles are closer together the capacity increases. 1 is another parameter that is important, and contributes along with 0 in the calculation of the safety distance maintained by the drivers in the simulation. 0 dominates at low speeds but 1 is very large if the speeds are relatively high. Lownes and Machemehl (2006) explained that as the desired distance between vehicles increases, the greater the distance that must be traversed as the vehicle resumes travel from a stopped or slowingmoving position. When speeds are high the difference in average capacity may not be as great. However, if the speeds are slow the increased distance between

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36 vehicles will have a direct effect on capacity (Lownes and Machemehl 2006) 1 is a factor that restricts the longitudinal oscillation of the vehicles in the simulation; it refers to the distance increment beyond the safety distance. Small values of 2 represent that drivers are more aggressive in their car -following behavior, meaning that the driver will speed up or slow down at a higher frequency (Lownes and Machemehl 2006) Lownes and Machemehl (20 06) discovered that if the driver is less aggressive and allows a larger distance to grow between vehicles the capacity of the roadway is reduced. This model takes into consideration that drivers are more alert when they are closer to the vehicle in front of them versus when they are further away. They considered the increase of the sensitivity related to the distance between the vehicles. However the Wiedemann model contained calibration parameters that is unclear how to calculate or their assumed values ranges. Fritzsche Fritzsche model is known as psycho physical model. This model is an example of a complex model, featuring twelve parameters to fit. The basic idea is to divide the car following plane into different regions, with different behaviors. The regions are: following I and II, emergency (the distance between vehicles is too small, so the follower will try to brake as hard as possible), approaching and driving freely. It could be seen easily, that any line in this plane is described by at least tw o parameters, so one readily ends up with twelve parameters. A variant of this model is being used with th e PARAMICS simulation software. In the model, the car -following process is categorized by five different modes shown in Figure 2-2 : the danger mode, t he closing in mode, the free driving mode, the

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37 following I mode, and the following II mode (Fritzsche 1994) Actions in each of the five modes are determined by speed thresholds and distance thresholds between two trailing vehicles, including perception thresholds of speed difference (PTN/PTP), desired distance (AD), risky distance (AR), safe distance (AS), and braking distance (AB). A positive perception threshold of speed difference (PTP) and a negative perception threshold of speed difference (PTN) are defined to distinguish two situations. When the speed of the following vehicle is faster than the speed of the vehicle immediately ahead of this vehicle (cal led leading vehicle), PTN is used. Whereas when the speed of the following vehicle is slower than that of the leading vehicle, PTP is introduced. In the danger mode, the distance between the following vehicle and the leading vehicle is below the risky dist ance. The following vehicle decelerates as much as possible to avoid a collision. In the closing in mode, the following vehicle travels at a faster speed than the leading vehicle and the actual speed difference is larger than PTN. The gap between the two vehicles is less than the desired distance but greater than the risky distance. Under this circumstance, the following vehicle decelerates until it slows down to the speed of the leading vehicle. There are two situations in the free driving mode: the following vehicle drives faster than the leading vehicle, but the gap between the two vehicles is larger than the desired distance, or the following vehicle is slower than the leading vehicle and the gap is larger than the risky distance. In both situations, the following vehicle accelerates to achieve its desired speed until it reaches another regime of thresholds.

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38 In the following I mode, when the actual speed difference is between PTN and PTP and the gap is greater than the risky distance and less than the desired distance, or when the actual speed difference is larger than PTP and the gap is greater than the risky distance and less than the safety distance, the following vehicle makes no conscious actions on deceleration or acceleration. In the following II mode, the speed of the following vehicle is faster than the leading vehicle and the actual speed difference is larger than PTN. However, the gap is larger than the desired distance or braking distance. Therefore, the following vehicle does not need to make any action and can drive freely. Figure 2-4 presents Olstam and Tapani default parameters relevant to the thresholds of Paramics. MITSIM The car -following used by MITSIM was based on previous research of Herman et al. (1959) It is describe as a stimulus-response model. The model is based on the headway and the relative speed between the lead and the following vehicles. Depending on the headway, a vehicle is classified into one of the three regimes: free following, car -following and emergency decelerating. Free flowing regime: If the time headway is larger than a pre determined threshold h_ upper the vehicle does not interact with the leading vehicle. In this case, if the vehicles current speed is lower than its maximum speed, it accelerates at the maximum acceleration rate to achieve its desir ed speed as quickly as possible. I f current speed is higher than the maximum speed, the vehicle decelerates with the normal deceleration rate in order to s low down.

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39 Emergency regime: If a vehicle has headway smaller than a pre determined threshold h_ lower it is in emergency regime. In this case, the vehicle uses an appropriate deceleration rate to avoid collision and extend its headway. Car -following regime: If a vehicle has headway betwe en h lower and h_ upper it is in the car -following regime. In this case the acceleration rate is calculated based on Hermans general car -following model (Ya ng and Koutsopoulos 1996) = ( 1) (2-12) W here: is the followers speed at time (t), 1 is the leads speed at time (t) is the spacing between the follower and the lead vehicle, and are six model parameters related to driver behavior to be calibrated for the car -following regime ( with values for acceleration and deceleration) Yang and Koutsopoulos (1996) discussed that the simpler version of MITSIM model utilized =0 and =1 but this value did not perform well in the model. May and Keller (1967) suggested values of =0.8 and =2.8 and Ozaki (1993) calibrated using 3 cars driving in a test track and suggested different values for accelerating and decelerating ( for accelerating +=0.2 and += 0.2 and for decelerating =0.9 and =1 ). However, Yang and Koutsopoulos (1996) suggested +=0.5 += 1 and += 1 for acceleration and =1. 25 =1 and =1 for deceleration. Punzo and Simonelli (2005) utilize the calibrations parameters and the h upper and h lower values shown in Figure 2-5.

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40 Modified P itt In an attempt to address the criticisms leveled at the P itt car -following model Cohen (2002) suggested a modification to the equation This modification of Pitt model is recognized as stimulus -response model. The Pitt car -following model assumes that the driver decisions are made in the interval the M odified P itt add a variable or that refers to the reaction time of the driver, therefore the time intervals will be + for the M odified P itt The modif ied approach equation now becomes: ( + ) = ( + ) ( + ) ( + ) + ( + ) ( + ) 1 2 ( + ) 2 ( + 1 2 ) (2-13) Where: = acceleration of the follower v ehicle = acceleration of the lead vehicle, = current simulation time = simulation time -scan interval = perception-reaction time (assumed equal for all vehicle) = sensitivity parameter used in modified P itt car -following model and = position of the lead and follower veh icle respectively at time t + R, = length of lead vehicle plus a buffer based on jam density = time headway parameter used in Pitt car -following model (refers to headway between rear bumper plus a buffer of lead vehic le to front bumper of follower), and = speed of the lead and follower veh icle respectively at time t + R Comparisons of Car -Following Models with Field Data This section summarizes previous research that has been conducted comparing car -following models with field data.

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41 The first two investigations comparing the car -following models with field data were by Chandler et al. (1958) and Herman et al. (1959) They compa red the GM model with data collected by wire linked vehicles. Subsequently Treiterer and Myers(1974) and Ozaki (1993) implemented an aerial technique to collect car -following data and calibrate the GM model. The results provided sensitivity parameters and for the GM model. However, the data contained high measurement errors due to the inaccuracy of the data collection method. Chundury and Wolshon (2000) analyzed the CORSIM car -following model with GPS field data collected on a two-lane highway in Baton Rouge, Louisiana for 72 min of total travel time. They recorded the data of two vehicles driving around a rectangular route near the LSU campus. Each vehicle was equipped with a GPS receiver, laptop computer, and GPS receiver antenna. Chundury and Wolshon (2000) found that under the given condition and their assumptions the NETSIM car -following model is accurate in simulating vehicle actions in routine driving conditions, and did not differ significantl y with the field data. However, they mentioned that it is necessary to study the use of a wider variety of driv er types to complete the study. Panwai and Dia (2005) evaluated AIMSUN, PARAMICS and VISSIM car -following models with data collected by Robert Bosch GmbH Research Group. The data used in the research paper was speed data under stopandgo traffic conditions on a singl e lane in Stuttgart, Germany during the afternoon peak hour. The Robert Bosch GmgH Research Group used an instrumented vehicle to record the difference in speed and headway between the instrumented vehicle and the vehicle immediately in front. The response of the follower vehicle (instrumented vehicle), in terms of acceleration and

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42 deceleration, was also recorded. They used the EM (Error Metric formulation) as the key performance indicator. They found that the results showed similar EM on distance values for the psychophysical spacing models used in VISSIM and PARAMICS with better values reported for the Gipps -based models implemented in AIMSUN. The Bosch data used the car -following behavior of only one driver, and the study area was a single lane urban road However, car -following behavior depends on the driver characteristics and driving environments such as number of lanes Panwai and Dia (2005) recommended further evaluation of these conditions. They also recommended conducting a sensitivity analysis to evaluate the impacts of simulation time step and different reaction times on the results. Punzo and Simonelli (2005) tested Newells model, Gipps model, a continuous response model (Intelligent Driver Model, IDM) and MITSIM model. The data they used was from Naples, Italy and they include two days of observation. For one of the days two different facilities were used : a one lane urban road and a two-lane suburban highway. The leader of the platoon was the author of th e research paper and the data were collected using four instrumented vehicles. If other vehicles intruded in the platoon, the data were discarded. They found that MITSIM is capable of reproducing the experimental data better that the other models with an average error of 12%, whereas the average error for IDM was 16%, and for Newel and Gipps 17%. Comparing these models, Punzo and Simonelli (2005) concluded that the Newell model performed the best on average but MITSIM showed a tendency to over fit the data due to the large number of parameters in the equation. For future research, they recommend analyze

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43 differ ent types of roads and traffic characteristics to confirm their findings with other experimental data sets. Ranjitkar et al. (2005) used a data set collected on a test track. Ten passengers participated in the experiment, the lead driver was a subject on his 50s, and the follower drivers were on their 20s and 30s. The data represent uninterrupted driving conditions with speeds ranging from 20 to 100 km/h. They concluded that the Chandler model performed better that the Gipps and Wiedemann models based on the tested conditions and the calibration parameters. Kim et al. (2007) analyzed the car -following behavior using an instrumented test vehicle equipped with four set of instrumentation, including an infrared sensor, GPSinertial distance measuring instrument (DMI), vehicle computer and a digital video camera. These data were collected during peak and nonpeak hour periods near Washington, D.C, for 301 car -following time series and an average duration of 99 seconds. The data tested in this research paper observed and analyzed the car following behavior of subjects that do not know they are part of the experiment. They concluded that there is an oscillatory process in car -following behavior formed by the vehicles de sired to keep their following distance. They also concluded that each individual driver has his or her driving rules rather than a deterministic driving law, and their distance can vary over time and space during different driving conditions. The reactions of the follower vehicle caused by the same maneuver in car -following situations repeat themselves over time and space. Rakha et al. (2010) develop a calibration procedure for CORSIM, AIMSUN, VISSIM, Paramics, and Integration using macroscopic loop detector data. They

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44 calibrate the steady -state component of this various car -following models, in another words when the lead vehicle is traveling at similar speeds and both the lead and the following having similar car -following behaviors. They concluded that the Gipps model and the Van Aerde (Integration car -following model) steady -state car following models provide the highest level of flexibility in capturing different driver and roadway characteristics. Literature Review Summary Many theories of car -following have been studied over the years were equations have been improved over time but as discussed in the literature review they assumed that all drivers follow the same driving behavior in different scenarios. These behaviors may differ with different drivers, or even for the same driver and with different conditions, and in fact, possibly with the same driver and nearly identical situations. All of the models examined so far use only a simple set of kinematic variables, such as relative spacing and speeds, instantaneous speeds, etc., to determine follower behavior. Table 2-4 provides a summary of the car -following model s with their description, equations and advantages and disadvantages. There are numerous other factors besides basic kinematics that may influence car -following behavior, such as congestion levels, geometric conditions, area type, time of day or week vari ous human characteristics (e.g., gender, age), and environmental characteristics (weather condition). Effects of road surface conditions and weather, traffic density, and different locations are related to the differences in car -following behavior. However, no further studies have been conducted to incorporate these factors into car -following models. For this reason, it is very important to compare trajectories obtained during different traffic conditions (congested vs. uncongested) and among different. The study

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45 goal is to provide recommendations regarding improvements to existing car -following models and their application.

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46 Figure 2-1 D ifferent thresholds and regimes in the Wiedemann car -following model (VISSIM 5.10 User gu ide) Table 2 -1 Parameters values for Wiedemann car -following model (Olstam and Tapani 2004) Parameter Description Value Reference AXadd Additive calibration parameter 1.25 (Wiedemann and Reiter, 1992) AXmult Multiplicative calibration parameter 2.5 (Wiedemann and Reiter, 1992) BXadd Additive calibration parameter 2 (Wiedemann and Reiter, 1992) BXmult Multiplicativ e calibration parameter 1 (Wiedemann and Reiter, 1992) EXadd Additive calibration parameter 1.5 (Wiedemann and Reiter, 1992) EXmult Multiplicative calibration parameter 0.55 (Wiedemann and Reiter, 1992) OPDVadd Additive calibration parameter 1.5 (Wiedem ann and Reiter, 1992) OPDVmult Multiplicative calibration parameter 1.5 (Wiedemann and Reiter, 1992) CX Calibration parameter 40* (PTV) BNullmult Multiplicative calibration parameter 0.1 (Wiedemann and Reiter, 1992) NRND Normal distributed random numbe r ( 0 5 0 15 ) ** (Wiedemann and Reiter, 1992) RND1 Normal distributed driver parameter ( 0 5 0 15 ) ** (Wiedemann and Reiter, 1992) RND2 Normal distributed driver parameter ( 0 5 0 15 ) ** (Wiedemann and Reiter, 1992) RND4 Normal distributed driver par ameter ( 0 5 0 15 ) ** (Wiedemann and Reiter, 1992) bmax Max acceleration 3 5 3 5 40 (Wiedemann and Reiter, 1992) bmin Max deceleration 20 1 5 60 (Wiedemann and Reiter, 1992) Estimation from graph ** Mean Values have been used

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47 Fi gure 2-2 Phase d iagram presenting the five different modes of Fritzsche car following model (Fritzsche 1994) Tabl e 2-2 Parameters values for Frizsche Car -following model (Olstam and Tapani 2004) Parameter Description Value Reference 1 Effective length, vehicle n -1 6 m (Fritzsche, 1994) Desired time gap 1.8 s (Fritzsche, 1994) 5_5_ Risky time gap 0.5 s (Fritzsche, 1994) 5`5` Safe time gap 1 s (Fritzsche, 1994) Deceleration parameter 0.4 m/ s 2 (Fritzsche, 1994) Calibration parameter 0.5* (Fritzsche, 1994) 5C5C Calibration parameter 0.001* (Fritzsche, 1994) 5C5C5C5C Calibration parameter 0.002* (Fritzsche, 1994) 5[5[5[5[5[5[ Acceleration parameter 0.2 m/s 2 (Fritzsch e, 1994) + Normal acceleration rate 2 m/s 2 (Fritzsche, 1994) Estimation from graph

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48 Table 2 -3 Parameters values for MITSIM c ar -following model (Punzo and Simonelli 2005) Model Parameter Mean Var Cv Gipps 3.331 4.189 0.614 3.801 5.949 0.642 4.783 10.613 0.681 16.152 12.28 0.217 0.567 0.024 0.272 MITSIM + 2.512 1.563 0.498 + 0.150 0.099 2.102 + 0.509 0.324 1.120 + 1.073 0.539 0.684 2.328 2.545 0.685 0.861 0.485 0.809 1.116 0.389 0.559 1.293 0.338 0.449 5b5b5b5b 2.044 0.285 0.261 5Y5Y5Y5Y 0.289 0.014 0.404 0.580 0.093 0.526 Var = variance Cv = covariance

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49 Table 2 -4 Summar y of c ar -following models Car following m odels Dependent v ariables Independent v ariables Forms of m odel Advantages Disadvantages Pipes (1950 ) Spacing + 1 ( follower speed ) +1 = + +1 + Easy to apply It ca n be used in lower speed situations Only describes the minimum distance between the vehicles (Dont consider reaction time) ( length of the lead vehicle ) Forbes (1950) Time Headway 5Z5Z5Z5Z 55 ( reaction Time) 5?5? ( L ength of vehicle) 5b5b ( sp eed of the lead vehicle) 5Z5Z5Z5Z = 55 + ( 5?5? / 5b5b ) Takes in consideration the needed follower reaction time to decelerate and apply the brakes It can be used in lower speeds situations Dont co nsider the desired speed o f the following vehicle and the dynamic elements such as behavior of the following ve hicle as a function of the lead vehicle. GM model (1958) Acceleration +1 Stimuli ( Vel. of lead and follower), Distance, React T ime, Sensitivity Parameter +1( + ) = [ +1( + ) ][ ( ) +1( ) ] [ ( ) +1( ) ] Take s in consideration stimulus response process This model doesnt recognize the desired of the following vehicle to drive faster Cant explain or implement the variation in the sensitivity values across different drivers Dont consider the effect of the inter vehicle spacing independently of the relative velocity. (It assumes that drivers will always accelerate if the relative velocity is + and decelerate if the relative velocity is In real driving, it is seen that when the follower is some reasonable distance behind the leading vehicle, the followin g vehicle can accelerate even if the relative velocity is zero. This wouldnt happen in high density traffic.)

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50 Table 2 -4 Continued Car following m odels Dependent v ariables Independent v ariables Forms of m odel Advantages Disadvantages (Newell 1961) Velocity ( FFS) (slope of spacing speed curve at =o) ( + ) = [1 ( 1( ) ( ) )] Consider the desired velocity of the follower vehicle. Dont consider the reaction time for the d rivers and sensitivity parameters. Consider that the characteristics of t he drivers and the roads are homogeneous. (Ga zi s et al 1961) (accel) ( relative speeds) ( ) = ( ) ( ) ( ) Considers the human f actors, It assumes that the follower reacts to the change in relative speeds a nd distances. Constant are difficult t o calibrate. It assumes that the follower reaction disappears when the relative speed is zero. (relative distance) (reaction t ime), (c onstants) (Gipps 1981) ( + ) Speed of vehicle n ( + ) = min ( ) +2.5 1 ( ) 0. 025 + ( ) 1 2 + 2[2 [ 1( ) 1( )] ( ) 1( )2 ]) } Mimic the behavior of real traffic. Speed calculations Considers the drivers characteristics as homogenous. Dont consider if the leading vehicle brakes harder than the following vehicl e or leaves the lane or when a new vehicle moves into the gap between the two vehicles (accel and deceleration emergency responses).

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51 Table 2 -4 Continued Car following m odels Dependent v ariables Independent v ariables Forms of m odel Advantages Disadvantages (Wiedemann and Reiter 1992) Spacing 1 time headway, vehicle speed 5c5c ve hicle length 5`5` = 0+ 1 + 5c5c + 2 / 2 C onsiders that drivers are more alert Considers the increase of the sensitivity Uses action points Difficult to approach a validity of these models because of the difficulty in calibrated the individual elements and thresholds Have 9 calibration parameters, some cases are assumed values. (Fritzsche 1994) Speed Twelve parameters 55 5]5]5]5]5]5] / 5]5]5]5]5]5] = 5>5>5>5>5>5> / 5]5]5]5]5]5] ( 55 ) + Accounts human perception in the definitions of the model regimes Complex model Twelve parameters to fit Takes in consideration the thresholds for the perception of speed differences Pitt 5N5N Spacing 5N5N = + 3. 04878 + + 5O5O ( )2 Considers N etwork characteristics Dont consider different reactions times and weather conditions Con siders each driver a unique desired headway

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52 Table 2 -4 Continued Car following m odels Dependent v ariables Independent v ariables Forms of m odel Advantages Disadv M ITSIM (1996) Response (Accel) Follower velocity = ( 1) Assumed m odel parameters 1 Lead v elocity Consider the desired follower speed. Have 6 calibration parameters providing a better fit of the data. Do not consider the tra ffic and weather conditions = gap distance Modified Pitt (2002) Acceleration K, Sf, Sl, L, h, vf, vl, al, T ( + ) = ( + ) ( + ) ( + ) + ( + ) ( + ) 1 2 ( + ) 2 ( + 1 2 ) Considers the reaction time of the driver s Do not consider different traffic and weather conditions

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53 CHAPTER 3 METHODOLOGY The research methodology developed for this thesis is illustrated in Figure 3-1 and described in this chapter. The methodology consists of six steps. These include a literature review of car -following models, selection of the models to be evaluated, initial implementation of the selected models in a spreadsheet program a ssembly of the data used in the study, data analysis, and conclusions and recommendations. The remaining of this chapter provides a brief overview of each step. Car -F ollowing M odels L iterature R eview A literature review was performed to review existing car -following models and their application. Each car -following model was identified and discussed highlighting their advantages and disadvantages. A review of their equations and parameters was included in Chapter 2 The literature review concluded with a tab le summarizing the car following models and their characteristics, as well as recommendations for future research. Selection of the M odels to be Evaluated Based on the car -following literature review four models were selected to be evaluated in this thesis After a process of evaluating the equations, parameters, and advantages and disadvantages the following four car -following models were selected: Gipps (Used in AIMSUN simulation program, m ulti regime model) Pitt model (Used in CORSIM, s timulus -response m odel) MITSIM model (Used in MIT simulation program s timulus -response model) Modified Pitt model (Modification of Pitt model) These models were selected because they are used in existing simulation programs and also because they are different from each ot her, representing various types of car -following models.

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54 Implementation of the Selected M odels The models were implemented in a spreadsheet program assuming the same lead vehicle trajectories, initial speed and distances. A comparison of trajectories and s peed differences was made between the resulting car -following trajectories for the four models. This initial implementation helped identify differences between the models and input s needed from the field data for further calibration Field D ata A ssembly Fi eld data were obtained from a database consisting of data collected in Jacksonville, Florida. Chapter 4 provides a detailed description of the original database and describes the data obtained for this research. The data were collected by cameras installed in a Honda Pilot SUV, and consist of video recordings of the speed, time and distances between the subject vehicle and its surrounding vehicles. Subjects of different gender and age were observed driving the instrumented vehicle. Th ese data capture various critical factors including driver behavior characteristics. The data were collected under different conditions (congested and uncongested), different times of day (AM/PM peak and off peak periods), and different weather conditions. Data were obtained for selected participants and conditions and organized for further analysis. Data A nalysis Two data analysis efforts were undertaken, an initial analysis and a calibration analysis. Each of these consist s of two steps. First, the l ead v ehicle t rajectory d ata for each selected participant and condition were entered in an spreadsheet In each of those file s the lead vehicle trajectories were the inputs, and the following vehicle trajectories were the outputs. Second, a comparison of the trajectories of the fie ld data and the estimated trajectories for each of the models was performed

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55 Initial Analysis During the init ial analysis, the model s were implemented using the default values of the parameters. The default values were those suggested in the original devel opment of each model After the implementation of the data, a comparison of the estimated trajectories for each model and the trajectories of the field data was made. Chapter 5 provides a detail ed discussion of the results for each of the selected models Calibration Analysis During the calibration analysis the parameters of each model were calibrated to fit the respective field data. The calibration analysis was performed using the optimization tool s olver in a spreadsheet program. Chapter 6 provides a d etailed description of this tool and the process used for the analysis. This analysis was divided in four different calibrations First each model was calibrated for each subject and each condition. In t he second calibration all the data were used. In the third calibration models were studied by different traffic conditions. The last calibration considered different driver types. Chapter 6 provides a detail ed discussion of the four calibration analysi s results for each model. Performance Measurement of Eac h Model Each of th e selected models predicts different kinematic variables. The Gipps model predicts the speed of the follower; the Pitt model predicts spacing between vehicles, while the MITSIM and Modified Pitt models predict the acceleration of the foll ower. I deally each scenario would be c alibrated using all three variables (speed, spacing and acceleration). Th is calibra tion would require multi objective optimization that w ould produce a nondominant optimum solution. It is difficult for practitioners t o perform this optimization. T herefore this analysis was completed taking in to

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56 consideration one variable at a time. T he two performance measures used in the calibration were follower speed and spacing between vehicles. To obtain a quantitative measure of the difference between the field data and the results of the selected models e rror test s were performed. Error tests do not contain any restriction or require assumptions about the data set. Most statistical tests require assumptions that the data are norm ally distributed and mutually independent. However, this is not the case with the data here. The distribution of data is not normal and the simulation and field data are not independent. The following vehicle start s with the same speed and position as in the field data. Therefore, the speed and position of vehicles depend on their previous values. In addition, the leader is the same in the field data as well as in the models. For this reason the results cannot be assumed to be mutually independent. Because of the above reasons, error tests are used to quantitatively measure the closeness of fit of results from the car -following models compared to the field data. The result is considered to be perfect, if values from simulation and field data are identical. The Root Mean Square Error (RMSE) test is one test which compares quantitatively the results from the car -following models results from field data. The RMSE was computed for the speed and spacing comparison for each of the selected models. The Root Mean Square Root is defined as follows: 5E5E = 2= ( )2 (3-1) Where is the exact solution (field data) is the computed solution (result from the models) is the total number of grid (ti me, s).

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57 The RMSE measures the deviation of the car -following model results value from the field data. The magnitude of error can be evaluated only by comparing it with the average size of the variable in question. An additional test that does not require comparison with the average size of variable is the RMS percent error defined as follows: 5E5E 5C5C5C5C5C5C5C5C5C5C5C5C 58585858585858585858 = 1 ( =1 100 )2 (3-2) The RMS percent error values tend to be large when smaller values are compared with larger differences. Similarly, it tends to be large when observed values are very small (Bham and Benekohal 2004). Another error test is the mean percent error, which is defined as follows: 5@5@5@5@5@5@5@5@ 5C5C5C5C5C5C5C5C5C5C5C5C 5858585858585\5\5\5\ = 1 ( =1 100 ) (3-3) The Mean percent error provides the deviation of car -following models results values from the field data as a percent, which provides a quantitative measure of deviation. However th e problem with percent errors is that they are close to zero if large positive errors cancel out large negative errors (Pindyck and Rubinfeld, 1998.) To av oid this problem both positive and negative percent errors are also calculated and used in the analysis as they are clearly present if the model is underestimating or overestimating compared to the observed values (Bham and Benekohal 2004). Mean absolute errors can also be calculated to avoid the problem of positive and negative errors canceling out but important information is lost when only the magnitude of errors is known. RMSE are used more often as they tend to penalize large individual errors

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58 more heavily (Pindyck and Rubinfeld 19 98 ). However, low RMSE are only one desirable measure of close fit to field data. Another statistic used in econometrics is Theils inequality coefficient, which is defined as follows (Pindyck and Rubinfeld n.d.) : = 1 ( )2 =1 1 ( )2 =1 + 1 ( )2 =1 (34) The numerator of U is the RMS error and the scaling of the denominator is such that U always falls between 0 and 1. If U =0 ( = ) for all then there is perfect fit. If U =1, the performance of the model is as bad as it can possibly be. Hence the Theils inequality coefficient measures the RMS error in relative terms. The RMS error percent, mean percent error and Theils inequality are not presented in this thesis, since their values were showing the same tendency as the RMSE. Therefore the analysis was done using the RMSE. Conclusions and R ecommendations In the last chapter, t his thesis provides calibration p arameters, application guidelines and suggested modifications related to each car -following model studied.

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59 Figure 3-1 Flowchart of the methodology Car following models literature review Selection of the models to be evaluated Field data assembly Implementation of the selected models in a spreadsheet program Data analysis Compare trajectories of field data and results of models Conclusions and Recommendations

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60 CHAPTER 4 DATA COLLECTION AND ANALYSIS PL AN The data collection and analysis plan for this thesis is presented in this chapter. This chapter will be divided in two main sections. The first section will presents the characteristics of the database used in this research. While, the second section w ill describe the method for selecting the data to be used and the procedures used to extract the data. Characteristics of the Database An instrumented vehicle was used to collect driver behavior data from 31 participants, in Jacksonville, Florida. The part icipants were asked to complete a background survey form that includes their driving habits and demographics information. The following subsections describe the instrumented vehicle used in the data collection, the driving routes and the subjects Instrume nted Vehicle The vehicle used to develop this database was a Honda Pilot SUV, owned by the University of Florida Transportation Research Center (TRC). The instrumented vehicle has a Honeywell Mobil Digital Recorder (HTDR400) system. This system has four wide coverage digital cameras, which capture front, rear, and side images which are recorded in the har d drive of the HTDR400 system. The vehicle also has a GPS where information of vehicle position and speed data is displayed and recorded on the HTDR400 system. The data that the instrumented vehicle can record include geographical position, speed, left -right turn signal activation, video clips and audio recording. A laptop is connected to the system and allows the display of the four

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61 cameras through the HTDR400 software. Figure 41 provides an internal view of the instrumented vehicle. Driving Routes The driving routes that participants followed in AM and PM peak periods are illustrated in Figure 42 and Figure 43. Each participant conducted two loops dur ing the AM routes and three during the PM routes. These locations were selected by Kondyli (2009) because there in mild to heavy traffic during the AM and PM peak periods, the routes were not complex and they were cameras from Jacksonville Traffic Operations Center. Description of the Database Subjects Participants of different gender and ages were selected to participate in the experiment. In addition, diff erent traffic and road scenarios, such as merging, lane changing, congested and uncongested scenarios, and weather conditions, such as rain were collected. The completion of each route was 1 hour to 1 hour and 15 minutes. Table 4 1 presents the characteris tics of the 31 subjects observed including gender, age, driving experience, how often they drive, time spent driving and the time of day when the data was collected. The data obtained through this database are related to the drivers and the environment sur rounding s Driver reaction times to events, categorization of drivers with respect to their degree of aggressiveness and relative distances and speeds were obtained from the instrumented vehicle. The process of extracting the data is described in the next section.

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62 Assembly of Data This section describes the process for selecting the subjects and the corresponding data to be used in this study. The following subsections describe the invehicle data processing and the distances, speed, and acceleration calcul ations for the field data. First, the researcher observed the time series of speed and flow provided by the Jacksonville Traffic Operations Center and Kondyli (2009) and identified the time periods where the freeway was congested (AM and PM) and when it wa s uncongested. Concurrently with the instrumented vehicle experiment, traffic -related data were collected. Speed time -series plots at all detector stations along the freeway segment were accessible in the database for all days of the data collection. Visua l observations of the time -series revealed the breakdown locations and times during the AM and the PM peak periods. It was also recorded in the database whether those time periods had rainy conditions. Drivers that drove under all scenarios were selected for further evaluation. Next, the researcher identified and categorized the time intervals by facility (e.g. d ivided the time intervals in arterial, freeway movements and on/off ramp movements ). Only the freeway intervals were considered in this study. The driver characteristics such as age, and gender were also obtained. To evaluate the aggressiveness of the driver the criteri a used by Kondyli ( 2009) were implemented. Three types of driver behavior were considered by Kondyli (2009) : aggressive, average and conservative behavior. The criterion of selfishness for each participant throughout the entire duration of their driving task was applied. Drivers that exhibit high degree of selfishness and consider primarily their own status on the road

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63 are regarded as aggressive. Drivers that act primarily as a response to the other vehicles actions are considered to be conservative. Drivers that consider both their own status but also the effect of their actions to the other vehicles are categorized as average. The driver types were quantitatively categorized on the following two criteria: (i) number of discretionary lane changes and (ii) observed speeds when driving under free-flowing and not car -following conditions. P articipants had generally limited opportunities for performing discretionary lane changes and for driving on the inside (faster) lanes. As such, participants that performed up to two lane changes and/or followed a speed 5 mi /h r (2.23 m/s) higher than the speed limit were considered to be conservative. Participants that performed up to five lane changes and/or drove at a speed up to 10 mi /h r (4.47 m/s) over the speed limit were considered to be average. Participants that performed at least six lane changes and/or drove at speeds up to 15 mi /h r (6.71 m/s) over the speed limit (or 10 mi /h r (4.47 m/s) over the limit under raining conditions) were categorized as aggressive. Table 4 -2 summarizes the results of the driver behavior analysis for all participants. This table also includes their background survey responses on their degree of a ggressiveness as this is perceived by themselves and by their friends or family, their stated driving sp eed and lane changing activity. The corresponding time intervals for congested and uncongested conditions for each driver were obtained and organized. N ext the data based on the longest time interval that one vehicle follows the same lead vehicle were selected. After organizing and recording the se time intervals, the researcher selected those with time intervals of at least 20 seconds. These time intervals were analyzed in depth on a secondby -

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64 second basis. Table 4 3 provides an example of the data obtained for a freeway interval and for a single vehicle. The next section provides a description of the process to obtain car -following information from the i nstrumented vehicle. Description of In-Vehicle Data Processing The video data collected from the instrumented vehicle cameras were used to estimate parameters related to spacing between vehicles and lead and follower vehicle speeds. The instrumented vehicle was the follower vehicle and only the front camera of the vehicle was used to obtain the spacing between the lead and follower. Images were extracted from the front camera at 1 s time resolution. When participants were following a vehicle the image extra ction would start and it would end as soon as one of three things occur ed: 1. The follower changes lanes and has a new leader 2. A new vehicle enters in front of follower 3. The 20 s of following the same lead vehicle was reached Along with the extracted frames, the instrumented vehicle (follower) speed was obtained from the GPS system. The following section presents the processing techniques to obtain the estimated distances between vehicles. Method for Extracting Information from the Digital Cameras The method us ed to obtain measurements of distance from the front camera is described in this section Procedures based on Psarianos et al. ( 2001) w ere implemented to extract the data from the cameras installed on the instrumented vehicle This method was developed for measuring lane widths but it was modified to account for distances along the road axis. This basic geometry is described in Figure 4-4 in which O is the perspective center and M is the image center.

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65 In Figure 44 the camera constant is while is the y image coordinate of points B and B 0 is the camera height measured above ground level, then the scale of the image at a distance is: = 0 = (4-1) Where: is the lane width BB, is the correspondin g length measured in the image. Equation 4-1 was first used to estimate the camera height 0 from known widths (range from 6 to 20 ft (1.83 m to 6.10 m) ) measured with a tape measure The camera height for the front camera is estimated as 3.96 ft 0.30 ft (1.21 m 0.09 m) Next, the camera constant was estimated for the front camera given known lane widths and distances according to Equation 42: = 0 = (4-2) Then, the constant of the camera was used for estimating the distance from any point of the road B by using the extracted images from the cameras. Distances, Speed and Acceleration Calculations A snapshot for each second was evaluated in AutoCad. Using AutoCad the researcher calculated the distances between the vehicles and using the camera constant described above the estimated distance was calculated. The distance between vehicles (subject/follower and the lead) is estimated for each consecutive frame using the method applied for measuring distances from still images explained in the previous subsection Although the distances obtained from the instrumented vehicle are approximations the values were close to the field data.

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66 However, an instrumented vehicle with infrared sensor will provide more accurately measures of distances. These distances are used for the calculations of the lead vehicle that will be the input for the model. Therefore, an estimation error may be affecting the final performance of the models. The follower/subject speed is directly obtained from the GPS T he acceleration is calc ulated as the speed change rate every second. The speed of the lead vehicle is estimated through consecutive frames using equations of motion. The lead speed was calculated as follows: 5?5?5?5?5?5? 5`5`5`5`5`5`5`5`5`5` =( 59595959595959595959595959595959 5`5`5`5`5`5`5`5`5`5` 1+ 595959595959595959595959 5R5R 5`5`5`5`5`5`5`5`5`5` ) 2 + ( 5F5F5F5F5F5F5F5F5F5F5F5F 5F5F5F5F5F5F5F5F5F5F5F5F 1) 5G5G5G5G5G5G (4-3) Table 4 4 presents second-by -second data for the time interval highlighted in Table 4 3. The second column of Table 4-3 presents the speed of the follower vehicle o btained from the GPS system. This speed was converted to meters per second to be used as inputs in the models tested. The fourth column (y -yf) provides the distances extracted using AutoCad from the still images of the video snapshots. The next two columns provide the spacing (in ft and in m) calculated using Equation 42 and solving for The last two columns provide the lead speeds (in mi /hr and in m/s) calculated using Equation 43. Table 4 5 presents the inputs used to obtain models estimates. T he lead vehicles speed for every second, and the follower vehicle speed and spacing d uring the first time interval are used as input in each car -following model. The highlighted area consists of output information which changes with every model.

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67 Fi gure 4-1 Inside view of the TRC instrumented vehicle

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68 Figure 4-2 AM r oute (Kondyli 2009) Table 4 -1 Description of Figure 4 -2 (Kondyli 2009) Number Description 1 Enter I 95 NB through Phillips Hwy on ramp 2 Exit at Baymeadows Rd. o f f ramp 3 Enter I 95 NB through Baymeadows Rd. on ramp 4 Exit at J.T. Bu tler off ramp 5 Stop at designated check point on J.T. Butler Blvd. 6 Enter I 95 NB through J.T. Butler on ramp 7 Exit at Bowden Rd. 8 Enter I 95 SB through Bowden Rd. on ramp 9 Exit at Phillips Hwy off ramp 10 Stop at designated check point on Phill ips Hwy (The Avenues Shopping Mall parking lot)

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69 Figure 4-3 PM r oute (Kondyli 2009) Table 4 -2 Description of F igure 4 -3 (Kondyli 2009) Number Description 1 Enter I 95 SB through Bowden Rd. on ramp 2 Exit at J.T. Butler Blvd. off ramp 3 Enter I 95 SB through J.T. Butler Blvd. on ramp 4 Exit at Baymeadows Rd. 5 Enter I 95 NB at Baymeadows Rd. 6 Exit at Bowden Rd. off ramp 7 Stop at designated check point on Bowden Rd. (parking lot)

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70 Table 4 -3 Characteristics of instr umented vehicle experiment participants (Kondyli 2009) Id Gender Age g roup Race Experience Occupation Driving f requency Hours per w eek Peak/ n on peak Vehicle o wnership 10 Male 55 65 Caucasian >=10 years Retired m ilitary Everyday 4 8 hrs Peak Pickup/suv 4 7 Male 25 35 Caucasian >=10 years Clerk Everyday 8 14 hrs Peak Sedan/coupe 49 Male 18 25 Caucasian 3 9 years Full time student Everyday <4 hrs Peak Sedan /coupe 52 Male 25 35 Caucasian >=10 years Professional driver Everyday 4 8 hrs Peak Pickup/suv 63 Ma le 25 35 Caucasian >=10 years Full time student Everyday 8 14 hrs Peak Pickup/suv 65 Male 25 35 Caucasian >=10 years Safety ranger Everyday <4 hrs Peak S edan/coupe 69 Female 25 35 Afr/ american >=10 years Full time student Everyday 4 8 hrs Peak Pickup/su v 71 Female 18 25 Asian caucasian 3 9 years Customer service Usually 4 8 hrs Peak Sedan/coupe 72 Male 25 35 Caucasian >=10 years Property manager Everyday 8 14 hrs Peak Sedan/coupe 73 Female 45 55 Caucasian >=10 years Office manager Everyday <4 hrs Peak Sedan/coupe 76 Male 25 35 Caucasian >=10 years University staff Never <4 hrs Non peak Sedan/coupe 23 Male 45 55 Caucasian >=10 years Military Usually 4 8 hrs Peak Pickup/suv 27 Male 45 55 Caucasian >=10 years Qual. Assurance Everyday 8 14 hrs Peak Seda n/coupe 32 Male 55 65 Caucasian >=10 years Pilot Sometimes 4 8 hrs Non peak Sedan/coupe 37 Female 45 55 Caucasian >=10 years Housewife Everyday 4 8 hrs Non peak Pickup/suv 51 Female 25 35 Caucasian >=10 years Admin. Assistant Everyday 4 8 hrs Peak Picku p/suv 59 Male 18 25 Asian 1 3 years Full time student Never <4 hrs Non peak Sedan/coupe 60 Male 45 55 Caucasian >=10 years Police officer Everyday 8 14 hrs Peak Sedan/coupe 61 Male 25 35 Caucasian >=10 years Pc refresh manager Everyday 8 14 hrs Peak Sed an/coupe 67 Male 35 45 Afr/ american >=10 years Cook Everyday 8 14 hrs Non peak Sedan/coupe 68 Female 18 25 Caucasian 1 3 years Full time student Everyday 4 8 hrs Peak Sedan/coupe 74 Female 45 55 Caucasian >=10 years Internet business Usually 8 14 hrs P eak Sedan/coupe 17 Female 45 55 Afr/ american >=10 years Secretary Everyday 8 14 hrs Peak Sedan/coupe 18 Female 35 45 Caucasian >=10 years Officer Everyday >14 hrs Peak Sedan/coupe 19 Female 45 55 Caucasian >=10 years Admin. Assistant Everyday <4 hrs Pe ak Pickup/suv 50 Female 25 35 Caucasian >=10 years Housewife Everyday 4 8 hrs Peak Pickup/suv 56 Male 35 45 Afr/ american >=10 years Sales Everyday 8 14 hrs Peak Sedan/coupe 58 Male 18 25 Caucasian 3 9 years Full time student Everyday 8 14 hrs Peak Seda n/coupe 66 Male 35 45 Asian 1 3 years Drafter Everyday <4 hrs Non peak Pickup/suv 70 Male 45 55 Caucasian >=10 years Professional driver Everyday >14 hrs Peak Sedan/coupe 75 Female 55 65 Caucasian >=10 years Sales & marketing Usually 8 14 hrs Peak Sedan /coupe

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71 Table 4 -4 Driver behavior types based on actual observations and background survey form (Kondyli 2009) Field observations Background survey responses Id DLC Driving (FFS) d Driver type Lane changing Driving speed Aggressiveness Aggressiveness by others 10 7 77 mi/h Aggressive Very often 75 to 80 mi/h Somewhat aggressive Somewhat aggressive 47 5 71 mi/h Aggressive Very often 70 to 75 mi/h Somewhat aggressive Somewhat conservative 49 16 72 mi/h Aggressive Very oft en 70 to 75 mi/h Somewhat aggressive Somewhat aggressive 52 6 68 mi/h (rain) Aggressive Very often 70 to 75 mi/h Somewhat aggressive Somewhat aggressive 63 12 78 mi/h Aggressive Sometimes 70 to 75 mi/h Somewhat conservative Very conservative 65 9 79 mi/ h Aggressive Very often 75 to 80 mi/h Somewhat aggressive Somewhat aggressive 69 16 67 mi/h (rain) Aggressive Sometimes 70 to 75 mi/h Somewhat conservative Very conservative 71 7 75 mi/h Aggressive Sometimes 70 to 75 mi/h Somewhat conservative Somewhat a ggressive 72 7 78 mi/h Aggressive Very often 70 to 75 mi/h Somewhat aggressive Somewhat aggressive 73 6 77 mi/h Aggressive Very often >80 mi/h Somewhat aggressive Very aggressive 76 6 79 mi/h Aggressive Very often 75 to 80 mi/h Somewhat aggressive Somew hat conservative 23 4 68 mi/h Average Very often 70 to 75 mi/h Somewhat conservative Very conservative 27 5 68 mi/h Average Sometimes 75 to 80 mi/h Somewhat aggressive Somewhat aggressive 32 4 71 mi/h Average Sometimes 75 to 80 mi/h Somewhat aggressive Somewhat conservative 37 4 71 mi/h Average Sometimes 70 to 75 mi/h Somewhat aggressive Somewhat aggressive 51 4 75 mi/h Average Very often 75 to 80 mi/h Somewhat conservative Somewhat aggressive 59 5 68 mi/h Average Sometimes 70 to 75 mi/h Somewhat aggr essive Very aggressive 60 4 71 mi/h Average Very often 70 to 75 mi/h Somewhat aggressive Somewhat aggressive 61 5 74 mi/h Average Very often 75 to 80 mi/h Somewhat aggressive Somewhat aggressive 67 4 73 mi/h Average Sometimes 75 to 80 mi/h Somewhat cons ervative Somewhat aggressive 68 4 70 mi/h Average Very often 70 to 75 mi/h Somewhat conservative Somewhat aggressive 74 4 72 mi/h Average Sometimes 70 to 75 mi/h Somewhat conservative Somewhat conservative 17 0 60 mi/h Conservative Sometimes < 65 mi/h V ery conservative Very conservative 18 2 70 mi/h Conservative Sometimes 70 to 75 mi/h Somewhat conservative Somewhat conservative 19 2 65 mi/h Conservative Sometimes 70 to 75 mi/h Somewhat conservative Somewhat conservative 50 2 71 mi/h Conservative Very often 70 to 75 mi/h Very conservative Somewhat conservative 56 2 67 mi/h Conservative Sometimes 70 to 75 mi/h Somewhat conservative i Somewhat aggressive 58 2 71 mi/h Conservative Sometimes 70 to 75 mi/h Somewhat conservative i Somewhat conservative 66 0 68 mi/h Conservative Sometimes 70 to 75 mi/h Somewhat conservative Somewhat conservative 70 2 69 mi/h Conservative Very often 70 to 75 mi/h Somewhat aggressive Very aggressive 75 1 70 mi/h Conservative Sometimes 70 t o 75 mi/h Somewhat conservative Somewhat conservative

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72 Table 4 -5 Trajectory of a single vehicle along with the corresponding conditions Time intervals Comments Difference 7:51:53 7:52:11 Right lane/ new car 0:00:18 7:52:12 7:52:22 Right lane/ new car 0:00:10 7:52:23 7:52:35 Right lane/ new car 0:00:12 7:52:36 7:52:39 Middle/ new car 0:00:03 7:52:40 7:53:33 Left/ new car 0:00:53 7:53:34 7:54:02 No cong/ left/ car 0:00:28 7:54:03 7:54:20 Left/ new car 0:00:17 7:58:25 7:5 8:31 Left/ car 0:00:06 7:58:32 7:58:35 Left/ new car] 0:00:03 7:58:36 8:02:35 Change lane/new car/ cong 0:03:59 8:02:36 8:04:29 New car/ con 0:01:53 8:04:30 8:05:20 New car/ con 0:00:50 8:08:53 8:10:21 Car/con/left 0:01:28 8:10:22 8:11:16 New car/ co ng/ left 0:00:54 A B Figure 4-4 Image geometry with A) H orizontal camera axis and B) M easurements on the digital image. (Psarianos et al. 2001)

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73 Table 4 -6 Second by second data for the time interval highlighted in Table 4 -3 Time Follower vehicle y-yf Gap Lead vehicle Speed Speed mi /hr m /s Spacing (ft) Spacing (m) mi /hr m /s 8:03:00 9 4.0 0.6463 44.21 13 .48 8:03:01 9 4.0 0.6266 45.60 13.90 9.9 4.421154817 8:03:02 9 4.0 0.6167 46.33 14.12 9.5 4.221804804 8:03:03 9 4.0 0.6258 45.65 13.92 8.5 3.795858182 8:03:04 9 4.0 0.6448 44.31 13.51 8.1 3.592344688 8:03:05 9 4.0 0.6356 44.95 13.70 9.4 4.19434752 8:03:06 9 4.0 0.626 45.64 13.91 9.5 4.208887814 8:03:07 10 4.5 0.6533 43.73 13.33 8.2 3.644291544 8:03:08 10 4.5 0.7074 40.39 12.31 7.7 3.430954033 8:03:09 10 4.5 0.6361 44.91 13.69 13.1 5.816270892 8:03:10 10 4.5 0.6635 43.06 13.13 8.7 3.882382304 8:03:11 11 4.9 0.6497 43.97 13.41 11.1 4.943823369 8:03:12 11 4.9 0.6515 43.85 13.37 10.9 4.852072151 8:03:13 11 4.9 0.722 39.57 12.06 8.1 3.591298584 8:03:14 12 5.4 0.701 40.76 12.43 12.3 5.470334141 8:03:15 12 5.4 0.7737 36.93 11.26 9.4 4.17283669 8:0 3:16 11 4.9 0.7676 37.22 11.35 11.7 5.200035802 8:03:17 11 4.9 0.754 37.89 11.55 11.5 5.092327175 8:03:18 10 4.5 0.7664 37.28 11.37 10.1 4.480888387 8:03:19 10 4.5 0.7592 37.63 11.47 10.2 4.551576859 8:03:20 10 4.5 0.7153 39.94 12.18 11.6 5.144318974 8:03:21 10 4.5 0.6701 42.64 13.00 11.8 5.260858898 8:03:22 10 4.5 0.6821 41.89 12.77 9.5 4.217147461 Table 4 -4 Inputs used in the implementation of each model Lead vehicle Follower vehicle Time (s) Accel Speed Pos Accel Speed Pos Spacing ft/s2 mi/h ft/s ft m ft/s2 mi/h ft/s m/s ft m ft m 1 0 9.95 14.59 45.60 13.9 0.00 9 13.20 4.02 0 0 45.6 13.9 2 9.50 13.93 3 8.54 12.53 4 8.08 11.85 9.44 13.84 9.47 13.89 n 8.20 12.03

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74 CHAPTER 5 INITIAL ANALYSIS AND RESULTS COMPARISON Initial analysis of the field data and results are presented in this chapter. The results for the Gipps, Pitt, MITSIM, and Modified P itt models were compared to the field data. The analysis was complet ed in a spreadsheet application The models were first analyzed with the default parameters used in the original references with a modification of the free flow speed of the follower vehicle and the length of the vehicle. A calculation example of each model application also is presented. The units used to present the calculations and results were the same units that the model was developed. Equivalent values in other system units are shown in parenthesis. Chapter 6 presents the model calibration undertaken where the parameters of each model were modified to obtain results as close as possible to the field data. This chapter is divided in five sections. The first four sections present the results of the implementation of the models in a spreadsheet program F inally, the last section provides a comparison of these four models. Gipps Model This section provides the assumptions used in applying the Gipps model and an example of its application. Detailed results by driver under different conditions are presented i n Appendix B Gipps (1981) defined the car following model as follows: ( + ) = min ( ) +2.5 1 ( ) 0. 025 +( ) 1 2 + 22[2 [ 1( ) 1( )] ( ) 1( )2 ]) } (5-1) Where:

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75 = maximum acceleration which the driver of vehicle n wishes to undertake (m/s2), = actual most severe deceleration rate that the driver of vehicle n wi shes to undertake ( < 0) (m/s2), = estimated most severe deceleration rate that the vehicle n -1 is willing to employ (m/s2), 1 = effective size of vehicle n; that is the physical length plus a margin into which the fol lowing vehicle is not willi ng to intrude even when at rest (m), 1 = speed at which the driver of vehicle n-1 wishes to travel (m/s), = speed at which the driver of vehicle n wishes to travel (m/s), ( ) = location of the front of vehicle n at time t (m), 1( ) = location of the front of vehicle n at time t (m), = speed at which the driver of vehicle n wishes to travel (m/s), = apparent reaction time, a constant fo r all vehicles (s). The assumptions used in this initial analysis were the following: is the maximum acceleration which the driver of vehicle n wishes to undertake = 2 m/s2 (4.47 mi /hr -s), is the actual mo st severe deceleration rate that the driver of vehicle n wishes to undertake ( < 0) = 3.0 m/s2 ( 6.7 mi /hr -s), is the estimated most severe deceleration rate that the vehicle n-1 is willing to employ = 3.50 m/s2 ( 7.83 mi /hr -s), 1 is the effective size of vehicle n; that is the physical length plus a margin into which the following vehicle is not willi ng to intrude even when at rest = 6.5m (21.33 ft), = speed at which the driver of vehicle n wishes to travel = Free Flow Speed (FFS) of each subject, = apparent reaction time, a constant for all vehicles = 0.667 s Table 5 1 presents all the inputs used which were obtained from the field data. The highlighted cells in the table consist of kinematics variables o f the lead and follower

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76 vehicle to be calculated. These were calculated with equations of motion and with the Gipps model. The results are provided in Table 5-2. The values in the second row are calculated with the following equations. The acceleration of the lead vehicle is calculated as follows: 5Y5Y5Y5Y5Y5Y ( )=( 5Y5Y5Y5Y5Y5Y ( ) 5Y5Y5Y5Y5Y5Y ( 1)) 5a5a5a5a5a5a (5-2) The acceleration of the lead vehicle in the second time interval (second and third column in Table 5 2) are calculated as follows: 5Y5Y5Y5Y5Y5Y ( 2 s ) = 4.2m s 4.4m s 1 s = 0.2m s2 ( 0.7ft s2 ) The position of the lead vehicle is calculated using the Equation 53. 5Y5Y5Y5Y5Y5Y ( )= ( 1)+ 5Y5Y5Y5Y5Y5Y ( 1) 5a5a5a5a5a5a + 0.5 5Y5Y5Y5Y5Y5Y ( ) 5a5a5a5a5a5a 2 (5-3) The position of the lead vehic le in the second time interval (sixth and seventh column in Table 5 2) is calculated as follows: 5Y5Y5Y5Y5Y5Y ( 2s ) = 13 .9 m+4.4m s 1s+ 0.5 ( 0.2m s2 ) ( 1s )2= 18. 25 m ( 59. 85 ft) The speed of the follower vehicle is calculated using the Equation 54. 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) = min 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) +2.5 1 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1 ) 0. 025 + 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1 ) 1 2 + 22[2 5Y5Y5Y5Y5Y5Y ( 1 ) 1 5S5S5S5S5S5S5S5S5S5S5S5S5_5_ ( 1 ) 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1 ) lead( 1 )2 ]) } (5-4) The speed of the follower vehicle in the second time interval (tenth and eleventh column in Table 52) is calculated as follows:

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77 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 2 s ) = 5Z5Z5Z5Z 4. 0 2m s +2.52m s2 0. 67 s 1 4. 02m s 32 .4m s 0. 025 +4. 02m s 32 .4m s 1 2 3.0m s2 0. 67 s+ 3.0m s2 2(0. 67 s)2 3.5m s2 [2 [ 13.9 m 6.5 m 0 m ] 4. 02m s 0. 67 5`5` 4. 22m s 2 3.5 m s 2 ]) = 5Z5Z5Z5Z 5. 1 5m s ,5.46m s =5. 15m s ( 16 .9ft s ) The acceleration of the follower vehicle is calculated using Equation 5-5. 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (t)=( 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1)) 5a5a5a5a5a5a (5-5) The acceleration of the follower vehicle in the second time interval (eighth and ninth column in Table 5 2) is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (2 s)= 5. 15m s 4. 02m s 1 s = 1. 13m s2 (3.7ft s2 ) The position of the follower vehicle is calculated using Equation 5-6. 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( )= ( 1)+ 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1) 5a5a5a5a5a5a + 0.5 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) 5G5G5G5G5G5G 2(5-6) The position of the follower vehicle in the second time interval (twelfth and thirteenth column in Table 5 2) is calculat ed as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (2s)=0 m+5. 15m s 1s+ 0.5 1. 13m s2 ( 1s )2=4.6 m ( 15 .0 ft) The spacing between vehicles is calculated using Equation 5-7. 5F5F5F5F5F5F5F5F5F5F5F5F ( ) = ( ) ( ) (5-7) The spacing between vehicles in the second time interval (fourteenth and fifteenth column in Table 5 2) is calculated as follows: 5F5F5F5F5F5F5F5F5F5F5F5F ( 2s ) = 18. 25 m 4.6 m= 13 .6 m ( 44 .7 ft)

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78 Gipps model predict ed the variable speed more accurately. The differences between the fie ld data and the Gipps speed result s were 4.47 mi /hr to 13.42 mi /hr (2m/s to 6m/s) On the other hand the differences between the spacing between vehicles were 9.84 ft to 207.9 ft (3.0 m to 63.38 m). Gipps car -following model predicts the follower speed thus it was expected that this variable was the best predicted by the model. In all of the cases the spacing was overestimated and the majority of the Gipps speed results were lower than the field data. The RSME values for speed were better than the spacing v alues. Comparing between conditions, the Gipps model predict ed the trajectories under congested scenarios more accurately The differences between the field data and the Gipps results for the follower speed in congested conditions were 4.47 mi /hr to 8.41 mi /hr (2 m/s to 3.76 m/s) and the differences for spacing were from 9.84 ft to 32.8 ft (3 m to 10.0 m) For uncongested the differences between the field data and the Gipps speed results were from 6.7 mi /hr to 13.42 mi /hr (3 m/s to 6 m/s) and for the differ ences between spacing were from 46.98 ft to 207.9 ft (14.32 m to 63.68 m) The RSME for spacing under rainy congested conditions varied from 2.17 to 3.80, for congested it varied from 1.60 to 3.73, and for uncongested and uncongested with rain were 5.49 to 20.81 and 8.29 to 45.92 respectively. Therefore the Gipps model predict ed congested conditions more accurately than uncongested. For rainy conditions the RSME for speed varied from 0.45 to 0.79, for congested conditions the RSME for speed was from 0.72 to 1.19 and for uncongested and uncongested with rain were 1.17 to 6.42 and from 1.54 to 2.69 respectively. The result of RSME for speed in rainy congested conditions was the

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79 lowest of all conditions. Gipps models predict ed rainy congested conditions more ac curate. Comparing between drivers, the results for the average driver were closer to the field data, having a lower value of RMSE for spacing and speed. The highest values of RMSE were for the most conservative ones or the most aggressive ones. The default s parameter values in the Gipps car -following model are better predicting average driver but a better calibration and analysis of the parameters is needed. Pitt Model This section provides the assumptions used in applying the Pitt model and an example of its application. Detailed results by driver under different conditions are presented in Appendix B. The Pitt model equation is as follows: 5N5N = + 3. 04878 + + 5O5O ( )2 (58) Where: 5N5N = space headway between the lead vehicle B and the follower A fr om front bumper to front bumper (m), = lead vehicle (B) length (m), = the car -following parameter (sensitivity factor) ( s), & = speed of vehicles lead and follower respectively (m/s), = calibration constant defined as 0.1(when > ) or 0 otherwise. The assumptions used in this initial analysis were the followin g: lead vehicle (B) length = 7.622 m (25 ft), the car -following parameter (sensitivity factor) for conservative drivers = 0.35 seconds, for aggressive drivers = 1.25 seconds (CORSIM Default distribution of car -following sensitivity factors)

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80 Table 51 presents all the inputs used which were obtained from the field data. The highlighted cells in the table consist of kinematics variables of the lead and follower vehicle to be calculated. These were calculated with equations of motion and with the Pitt model. The results are provided in Table 5-3. The acceleration and position of the lead vehicle were calculated with Equation 52 and Equation 53 respectively. The spacing (last column in Table 5 -3 ) are calculated using Equation 5-9. 5N5N ( ) = + 3. 04878 + 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1) + 5O5O ( 5Y5Y5Y5Y5Y5Y ( 1) 5S5S5S5S5S5S5S5S5S5S5S5S ( 1) )2 (5-9) Where: = calibration constant defined as 0.1(when 5S5S5S5S5S5S5S5S5S5S5S5S5S5S > 5Y5Y5Y5Y5Y5Y ) or 0 otherwise The spacing between vehicles in the second time interval ( last columns in Table 5-3 ) is calculated as follows: The 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1) < 5Y5Y5Y5Y5Y5Y ( 1) therefore = 0 5N5N ( 2 s ) = 7. 62m + 3. 04878 + 0. 35 5`5` 4. 0 2 5`5` + 00. 35 5`5` (4. 4 21 / 5`5` 4. 0 2 m/s )2= 12 .1 m ( 39.6 ft) The position of the follower vehicle is calculated using the following equation: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) = 5Y5Y5Y5Y5Y5Y ( ) 5N5N ( ) (5-10 ) The position of the follower vehicle in the second time interval is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 2s ) = 18 .2 m 12 .1 m=6.1 m ( 20 .1 ft) The speed of the follower vehicle is calculated using Equation 5 -11. 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (t)= (t 1)2+ 2 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( t 1 ) ( 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) 5S5S5S5S5S5S5S5S5d5d5d5d5d5d ( 1 ) ) (5-11) T he speed of the follower vehicle in the second time interval (tenth and eleventh column Table 5 3) is calculated as follows:

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81 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 2s ) = 4. 02m s 2+ 22m s2 ( 6.1 m 0 m ) =5.3m s ( 17 .5ft s ) The acceleration of the follower vehicle is calculated using Equation 5-12. 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (t)=( 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1)) 5a5a5a5a5a5a (5-12 ) The acceleration of the follower vehicle in the second time interval (eighth and ninth column Table 5 -3 ) is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (2 s)= 5.3m s 4. 02m s 1 s = 1.3m s2 (4.3ft s2 ) For some subjects the Pitt model predicted more accurately the variable speed and for others the spacing variable. However the overall RMSE was lower for the speed variable. The differences between the field data and the Pitt result for speed were from 7 mi /hr to 32.7 mi /hr (3.13 m/s to 14.62 m/s) The differences between the field data and the Pitt result for the spacing were from 7.22 ft to 85 ft (2.20 m to 25.88 m) For all the subjects in all conditions Pitt model predicted a higher speed than the field data. The spacing between vehicles in some intervals was higher than the field data and in other was lower. Com paring between conditions, the Pitt model predict ed the trajectories under congested conditions more accurately The differences between the field data and the Pitt results for speed under congested conditions were from 7 mi /hr to 32.7 mi /hr (3.13 m/s to 1 4.62 m/s) and the differences for spacing were from 7.22ft to 49.54 ft (2.20 m to 15.10 m). For uncongested the differences between the field data and the Pitt speed results were from 9.77 mi /hr to 31.6 mi /hr (4.37 m/s to 14.16 m/s) and for the differences between spacing were from 14.4 ft to 85 ft (4.39 m to 25.91 m) Pitt model predicted the trajectories of the vehicles for the congested scenarios more accurately

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82 than the overall uncongested scenarios. The RSME for spacing in rainy congested conditions va ried from 1.22 to 4.06. T he RSME for spacing in congested it varied from 2.19 to 9.18, and for uncongested and uncongested with rain were 2.54 to 15.93 and 8.51 to 14.98 respectively. Therefore the Pitt model predict ed congested conditions more accurately than uncongested. The RSME for speed was higher than the RSME for spacing for rainy congested conditions H owever for uncongested and congested conditions the RSME for speed was lower than spacing. For the rainy congested the RSME for speed varied from 1.89 to 5.36. For congested conditions the RSME for speed was from 1.25 to 10.36 and for uncongested and uncongested with rain were 2.77 to 10.15 and from 6.98 to 13.52 respectively. The results of RSME for speed in rainy congested conditions were the lowest of all, concluding that the Pitt models predicted the congested rainy conditions more accurate Comparing between drivers, Pitt model predicted a better sp acing and speed for conservative and aggressive drivers However the lowest overall RSME for spacing and speed in each condition was for the aggressive drivers. The defaults parameter values in the Pitt car -following model are better predicting conservative and aggressive driver but a better calibration and analysis of the parameters is needed. MITSIM Mod el This section provides the assumptions used in applying the MITSIM model and an example of its application. Detailed results by driver under different conditions are presented in Appendix B. MITSIM car -following model is defined as follows: = ( 1) (5-13 ) Where:

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83 = followers speed (m/s) 1 = leads speed (m/s), = spacing between the follow er and the lead vehicle minus the lead vehicle length, = 1 1 (m), 5N5N5N5N = six model parameters related to driver behavior to be calibrated for the car -following regime ( with values for acceleration and deceleration) The assumptions used in this initial analysis were the following: 1, lead vehicle length = 7.62 m (25 ft) 5N5N5N5N six model parameters related to driver behavior to be calibrated for the car -following regime ( with values + for acceleration when 5S5S5S5S5S5S5S5S5S5S5S5S5S5S 5Y5Y5Y5Y5Y5Y and f or deceleration when 5S5S5S5S5S5S5S5S5S5S5S5S5S5S > 5Y5Y5Y5Y5Y5Y ) = +=0.5 += 1 and += 1 and =1. 25 =1 and =1 Table 5 1 presents all the inputs used which were obtained from the field data. The highlighted cells in the table consist of kinematics variables of the lead and follower vehicle to be calculated. These were calculated with equations of motion and with the MITSIM model. The results are provided in Table 54. The acceleration and position of the lead vehicle were calcula ted with Equation 5-2 and Equation 5-3 respectively. The values in the second row are calculated with the following equations. The acceleration of the follower is calculated using Equation 514. 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (t)= 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 5Y5Y5Y5Y5Y5Y (t 1) 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (t 1)) (5-14) Where: 5N5N5N5N six model parameters related to driver behavior to be calibrated for the car -following r egime ( with values + for acceleration when 5S5S5S5S5S5S5S5S5S5S5S5S5S5S 5Y5Y5Y5Y5Y5Y and for deceleration when 5S5S5S5S5S5S5S5S5S5S5S5S5S5S > 5Y5Y5Y5Y5Y5Y ) = +=0.5 += 1 and += 1 and =1. 25, =1 and =1

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84 The acceleration of the foll ower vehicle in the second time interval (eighth and ninth column Table 5 -4) is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S 5Y5Y5Y5Y5Y5Y = used values + for acceleration = +=0.5 += 1 and += 1 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( t ) = 0.5 4. 02m s 1( 13 .9 m ) 1 4. 421m s 4. 02m s =0. 69 / 5`5` 2(2. 27ft 5`5` 2 ) The speed of the follower is calculated using the following equation: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (t)= (t 1)+ 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (t) time (5-15) The speed of the follower vehicle in the second time interval (tenth and eleventh column Table 5 4) is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 2s ) =4. 02m s + 0. 69 m/ 5`5` 2 1 sec =4.7m s ( 15 .5 ft/s) The position of the follower is calculated using Equation 5-16 5\5\5\5\5\5\5\5\5\5\5\5\5\5\ ( )= ( 1)+ 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 1) 5a5a5a5a5a5a + 0.5 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) 5G5G5G5G5G5G 2 (516) The position of the follower vehicle in the second time interval is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (2s)=0 ft+4. 02m s 1 sec + 0.5 0. 69m s2 ( 1s )2=4. 37 m ( 14 .3 ft) The spacing between vehicles is calculated using the following equation: 5F5F5F5F5F5F5F5F5F5F5F5F ( ) = ( ) ( ) (5-17) The spacing between vehicles in the second time interv al ( lasts column in Table 5 4) is calculated as follows: 5F5F5F5F5F5F5F5F5F5F5F5F ( 2s ) = 18.2 m 4.4 m= 13 .9 m ( 45 .4 ft) MITSIM model predict ed the variable speed more accurately. The differences between the field data and the MITSIM model result for speed were from 2.57 mi /hr to 10.5 mi /hr (1.15 m/s to 4.69 m/s ). O n the other hand the differences between the spacing were from 8.9 ft to 65 ft (2.71 m to 19.82 m) The RSME values for speed were better than the spacing values.

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85 Comparing between conditions, MITSIM model predicted the trajectories under congested s cenarios more accurately The differences between the field data and the MITSIM results for speed under congested scenarios were from 2.57 mi /hr to 6.8 mi /hr (1.15 m/s to 3.04 m/s) and the differences for spacing were from 8.9 ft to 43.6 ft (2.71 m to 13.29 m). For uncongested the differences between the field data and the MITSIM speed results were from 6 mi /hr to 10.5 mi /hr (2.68 m/s to 4.69 m/s) and for the differences between spacing were from 30 ft to 65 ft (9.14 m to 19.82 m) The RSME for spacing under rainy congested conditions varie d from 1.28 to 2.85, for congested conditions it varied from 1.67 to 6.77 and for uncongested and rain uncongested were 6.18 to 14.98 and 4.62 to 10.47 respectively. The RSME for speed comparison was lower than the RSME for spacing, consistent with other models For the r ain congested the RSME for speed varied from 0.46 to 0.93, for congested conditions was from 0. 82 to 1.19 and for uncongested and rain uncongested were 1.05 to 2.10 and from 1.09 to 2.83 respectively. The result of RSME for speed in rainy congested conditions was the lowest of all. MITSIM models predict ed the rainy congested conditions more accurate. Comparing between driver types the highest values of RMSE for spacing were for the conservative and aggressive drivers On the other hand the highest values of RSME for speed were for the average drivers The lowest values of RSME for spacing were for aggressive driver s and the lowest values of RMSE for spacing were for average drivers. For a better understanding of these behavior a better calibration and analysis of the parameters is needed.

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86 Modified P itt Model This section provides the assumptions used in applying the Modified Pitt model and an example of its appli cation Detailed results by driver under different conditions are presented in Appendix B. Cohen, (2002) defined the Modified P itt car following model as follows: ( + ) = ( + ) ( + ) ( + ) + ( + ) ( + ) 1 2 ( + ) 2 ( + 1 2 ) (518) Where: = acceleration of the follower vehicle (ft/s2), = acceleration of the lead vehicle (ft/s2), = current simulation time (s), = simulation time -scan interval (s), = perception-reaction time (assumed equal for all vehicle) (s), = sensitivity parameter used in M odified P itt car following model and = position of the lead and follower vehicle respectively at time t + R (ft), = length of lead vehicle plus a buffer based on jam density (ft), = time headway parameter used in Pitt car following model (refers to headway between rear bumper plus a buffer of lead vehic le to front bumper of follower) ( s), and = speed of the lead and follower veh icle respectively at time t + R (ft/s). The assumptions used in this initial analysis were the following: simulation time -scan interval = 1 s perception -reaction time (assumed equal for all vehicle) = 1 s sensitivi ty parameter used in modified P itt car following model = 0.35 length of lead vehicle plus a buffer based on jam density = 32 ft time headway parameter used in Pitt car following model = 1.5 s

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87 An example of the calculation process is described below. The calculations for two time intervals are discussed. Table 5 1 presents all the inputs used which were obtained from the field data. The highlighted cells in the table consist of kinematics variables of the lead and follower vehicle to be calculate d. These were calculated with equations of motion and with the Modified Pitt model. The re sults are provided in Table 5 5. The acceleration and position of the lead vehicle were calculated with Equation 5-2 and Equation 5 -3 respectively. The values in the second row are calculated with the following equations. The acceleration of the follower vehicle is calculated using Equation 5-19. 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( + )= ( ) ( ) ( ) + ( ) ( ) 1 2 ( + ) 2 ( + 1 2 ) (5-19) The acceleration of the follower vehicle in the second time interval (sixth column Table 5-5) is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (2 5`5` )= 0. 35 45 60 ft 0 ft 32 ft 1.5s 13 .2ft s + 13 .2ft s 14. 58 ft s 1s 1 2 0. 65 ft /s21s2 1s (1.5s+ 1 2 1s ) = 1. 271 ft/s2( 0. 3875m s2 ) The speed of the follower vehicle is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( +R)= ( )+ 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( +R) time (5-20) The speed of the follower vehicle in the second time interval (seventh column Table 55) is calculated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( 2s ) = 14 58ft s 1. 271 1s= 11. 93ft s (3. 637 m/s) The position of the follower vehicle is calculates using the following equation: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( + )= ( )+ 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( ) 5a5a5a5a5a5a + 0.5 5S5S5S5S5S5S5S5S5S5S5S5S5S5S ( + ) 5G5G5G5G5G5G 2(5-21)

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88 The position of the follower vehicle in the second time interval (ninth column Table 5 -5) is calcul ated as follows: 5S5S5S5S5S5S5S5S5S5S5S5S5S5S (2s)=0 ft+ 13 .2ft s 1s+ 0.5 ( 1. 271ft s2 ) ( 1s )2= 12 56 ft (3. 83 m) The spacing between vehicles is calculated using Equation 5-22 5F5F5F5F5F5F5F5F5F5F5F5F ( + ) = ( + ) ( + ) (5-22) Th e spacing between vehicles in the second time interval (last column in Table 5 5) is calculated as follows: 5F5F5F5F5F5F5F5F5F5F5F5F ( 2s ) = 59. 85 ft 12 56 ft= 47 29 ft ( 14 41 m) Modified Pitt model predict ed the variable speed more accurately The differences betwe en the field data and the Modified Pitt result for speed were from 1.95 mi /hr to 34.39 mi /hr ( 0.87 m/s to 15.38 m/s) On the other hand the differences between the spacing were from 55.92 ft to 2 31.37 ft (17.05 m to 38.38 m). The speed results were more ac curate than the spacing. Modified Pitt assumes that the follower vehicle will maintain a minimum safe distance. This safe distance is calculated as follows: 5F5F5F5F5F5F 5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q = 5S5S5S5S5S5S5S5S5S5S5S5S5S5S 5`5`5`5`5`5`5`5`5`5` ( + ) (523) If this safe distance is calculated for the first interval the value will be: 5F5F5F5F5F5F 5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q5Q =1.5s 1 4 58ft s = 21 87 ft (6. 66 m) This safe distance value is higher than the actual spacing that the follower vehicle is using (13.2 ft, 4.02 m) Therefore from the first interval the Modified Pitt is assuming a distance that is much bigger, consequently the other intervals are going to be affected by this assumption. For a bet ter understanding of these behavior a better calibration and analysis of the parameters is needed

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89 Comparing between conditions, the Modified Pitt model predict ed more accurately the trajectories in congested conditions The differences between the field data and the Modified Pitt results for speed under congested scenarios were from 1.95 mi /hr to 15.21 mi /hr ( 0.87 m/s to 6.80 m/s) and the differences for spacing were from 19.15 ft to 78.56 ft (5.84 m to 23.95 m) For uncongested the differences between th e field data and the Modified Pitt model speed results were from 8.94 mi /hr to 33.50 mi /hr (4 m/s to 14.98 m/s) and for the differences between spacing were from 58.48 ft to 23 1.37 ft (17.53 m to 70.54 m) The RSME for spacing in rainy congested varie d from 9.44 to 13.4, congested conditions v aried from 3.83 to 12.13, and for uncongested and rain uncongested were 20.84 t o 43.15 and 8.13 to 36.23 respectively. The RSME for speed comparison were lower than the RSME for spacing, being consistent with the other models results. For the rain uncongested the RSME for speed varied from 2.36 to 3.58, for congested conditions the RSME for speed was from 0.41 to 3.53 and for uncongested and rain uncongested were 6.83 to 10.56 and from 3.81 to 9 respectively. The result of RSME for speed in congested conditions was the lowest of all conditions. The Modified Pitt models predict ed the congested conditions more accurate. Comparing between driver types the results for the average driver were closer to the field data, having a lower value of RMSE for spacing and speed. The highest values of RMSE were for the most conservative ones. The defaults values of the parameters in the Modified Pitt car -following model were better predicting average driver but a better calibration and analysis of the parameters is needed.

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90 Summary of the Initial Analysis Figure 51 to 5-8 provides comparison graphs of different conditions for the average driver. From these Figures and the results discussed above, it can be concluded that all the models pr edicted more accurately the follower speed. The RMSE values for speed overall were lower than the RMSE for spacing. The model with the lowest difference between the speed and the field data was MITSIM with an overall RMSE of 111 for spacing and 23.84 for s peed Pitt model has the highest difference between the speed and the field data (RMSE speed value of 97.15), and Modified Pitt the highest difference in spacing (RMSE spacing value of 342.14). From the Figures 5-1 to 5 8 it can be concluded that c omparing between conditions, all the models predicted better the congested conditions than the uncongested scenario. MITSIM was the best model to predict the congested conditions. For un congested conditions, the model that predicts more accurately the speed was MI TSIM and for the spacing was P itt In addition f or the two congested conditions (rain congested and congested) the rain congested was more accurately to the field data, except for Modified Pitt that predicted better the congested condition. Comparing bet ween driver type s, overall the average driver was the closest to the field data, and the highest vales of RMSE were for the conservative and the aggressive driver. The results showed that the best model predicting the average driver behavior was MITSIM and for the aggressive and conservative drivers the spacing was best predicted by Pitt and the speed by MITSIM. These results were using the default values of each model thus a better calibration and analysis of the parameters is needed

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91 Table 5 -1 Inputs used in the implementation of each model Time (s) Lead v ehicle Follower v ehicle Spacing Ac el Speed Position Ac el Speed Position m/s2 ft/s2 m/s ft/s ft m m/s2 ft/s2 ft/s m/s mi /hr ft m ft m 1 0 0 4.4 14.5 45.6 13.9 0 0 13.2 4.0 9.0 0 0 45.6 13.9 2 4. 2 13. 9 3.8 12. 5 3. 5 11. 8 n 4. 2 13. 8 Hi ghlighted cells will be the different outputs of each model Table 5 -2 Results of the Gipps model implementation Time (s) Lead v ehicle Follower v ehicle Spacing Accel Speed Position Accel Speed Position m/s 2 ft/s 2 m/s ft/s ft m m/s 2 ft/s 2 ft/s m/s ft m ft m 1 0.0 0.0 4.4 14.5 45.6 13.9 0.0 0.0 13.2 4.0 0.0 0.0 45.6 13.9 2 0.2 0.7 4.2 13.8 59.8 18.2 1.1 3.7 16.9 5.2 15.0 4.6 44.7 13.6 3 0.4 1.4 3.8 12.5 72.9 22.2 0.0 0.1 16.8 5.1 31.9 9.7 41.0 12.5 4 0.2 0.7 3.6 11.8 85.0 25.9 0.9 2.9 13.9 4.2 47.3 14.4 37.8 11.5 5 0.6 2.0 4.2 13.8 97.8 2 9.8 0.1 0.4 13.5 4.1 60.9 18.6 36.9 11.2 Table 5 -3 Results of the Pitt model implementation Time (s) Lead v ehicle Follower v ehicle Spacing Accel Speed Position Accel Speed Position m/s 2 ft/s 2 m/s ft/s ft m m/s 2 ft/s 2 ft/s m/s ft m ft m 1 0.0 0.0 4.4 14.5 45.6 13.9 0.0 0.0 13.2 4.0 0.0 0.0 45.6 13.9 2 0.2 0.7 4.2 13.8 59.8 18.2 1.3 4.3 17.5 5.3 20.1 6.1 39.6 12.1 3 0.4 1.4 3.8 12.5 72.9 22.2 0.8 2.7 20.2 6.2 31.6 9.6 41.3 12.6 4 0.2 0.7 3.6 11.8 85.0 25.9 0.4 1.3 21.6 6.6 42.3 12.9 42.7 13.0 5 0.6 2.0 4.2 13.8 97.8 29.8 0.2 0.7 22.3 6.8 54.2 16.5 43.6 13.3

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92 Table 5 -4 Results of the MITSIM model implementation Time (s) Lead v ehicle Follower v ehicle Spacing Accel Speed Position Accel Speed Position m/s 2 ft/s 2 m/s ft/s ft m m/s 2 ft/s 2 ft/s m/s ft m ft m 1 0.0 0.0 4.4 14.5 45.6 13.9 0.0 0.0 13.2 4.0 0.0 0.0 45.6 13.9 2 0.2 0.7 4.2 13.8 59.8 18.2 0.7 2.3 15.5 4.7 14.3 4.4 45.4 13.9 3 0.4 1.4 3.8 12.5 72.9 22.2 0.5 1.5 1 3.9 4.2 29.0 8.8 43.9 13.4 4 0.2 0.7 3.6 11.8 85.0 25.9 0.4 1.4 12.6 3.8 42.3 12.9 42.8 13.0 5 0.6 2.0 4.2 13.8 97.8 29.8 0.2 0.7 11.9 3.6 54.5 16.6 43.3 13.2 Table 5 -5 Results of the Modified Pitt model implementation Time (s) Lead v ehicle Follower v ehicle Spacing Accel (ft/s 2 ) Speed (ft/s) Pos (ft) Pos (m) Accel (ft/s 2 ) Speed (ft/s) Speed (m/s) Pos (ft) Pos (m) ft m 1 0.0 14.5 45.6 13.9 0.0 13.2 4.0 0.0 0.0 45.6 13.9 2 0. 7 13. 8 59.8 18.2 1. 3 11.9 3.6 12. 6 3.8 4 7. 3 14.4 3 1.4 12.5 72. 9 22.2 0. 7 11. 3 3.4 24. 2 7. 4 48.9 14.9 4 0.7 11.8 85. 0 25.9 0.1 11. 1 3. 4 35.3 10. 8 50.0 15.2 5 2.0 13.8 97.8 29. 8 0. 1 11.0 3. 4 46. 4 14.1 51. 8 15.8

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93 Figure 5-1 Spacing between lead and follower vehicle for each time interval (u ncongested condition, s ubject 67) Figure 5-2 Follower vehicle speed for each time interval ( u ncongested condition, s ubject 67) 0 10 20 30 40 50 60 70 0 5 10 15 20Spacing (meters)Time (sec) Spacing between lead and follower vehicle (uncongested conditions, average driver) Field data Gipps model Pitt Model MITSIM Model Modified Pitt Model 0 10 20 30 40 50 60 70 0 5 10 15 20Speed (m/s)Time (sec) Follower vehicle speed (uncongested conditions, average driver) Field Data Gipps Model Pitt Model MITSIM Model Modified Pitt Model

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94 Figure 5-3 Spacing between lead and follower vehicle for each tim e interval (c ongested condition, s ubject 67) Figure 5-4 Follower vehicle speed for each time interval ( c ongested condition, s ubject 67) 0 10 20 30 40 50 60 70 0 5 10 15 20Spacing (meters)Time (sec) Spacing between lead and follower vehicle (congested conditions, average driver) Field Data Gipps Model Pitt Model MITSIM Model Modified Pitt Model 0 10 20 30 40 50 60 70 0 5 10 15 20Speed (m/s)Time (sec) Follower vehicle speed (congested conditions, average driver) Field Data Gipps Model Pitt Model MITSIM Model Modified Pitt Model

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95 Figure 5-5 Spac ing between lead and follower vehicle for each time interval ( r ain u ncongested condition, s ubject 67) Figure 5-6 Follower vehicle speed for each time interval ( r ain u ncongested condition, s ubject 67) 0 10 20 30 40 50 60 70 0 5 10 15 20Spacing (meters)Time (sec) Spacing between lead and follower vehicle (rain uncongested condition, average driver) Field data Gipps Model Pitt Model MITSIM Model Modified Pitt Model 0 10 20 30 40 50 60 70 0 5 10 15 20Speed (m/s)Time (sec) Follower vehicle speed (rain uncongested condition, average driver) Field data Gipps Model MITSIM Model Pitt Model Modified Pitt Model

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96 Figure 5-7 Spacing between lead and follower vehicle for each time interval ( r ain c ongested condition, s ubject 67) Figure 5-8 Follower vehicle speed for each time interval ( r ain c ongested condition, s ubject 67) 0 10 20 30 40 50 60 70 0 5 10 15 20Spacing (meters)Time (sec) Spacing between lead and follower vehicle (rain congested conditions, average driver) Field data Gipp Model Pitt Model MITSIM Model Modified Pitt Model 0 10 20 30 40 50 60 70 0 5 10 15 20Speed (m/s)Time (sec) Follower vehicle speed (rain congested conditions, average driver) Field data Gipp Model Pitt Model MITSIM Model Modified Pitt Model

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97 C HAPTER 6 CALIBRATION ANALYSIS This chapter provides a calibration analysis for the parameters of each car following model. Based on the initial analysis, calibration of the parameters for each model was conducted by minimizing the RMSE for speed and spacing differences. The optimization tool in a spreadsheet program was used to provide values of the parameters that minimize the RMSE value. As mentioned in Chapter 5 the closest to zero the value of RMSE is, the closest the results of the models will be to th e field data. The optimization tool in called s olver includes input locations to specify the solution or target cell location, and whether the goal is to maximize, minimize, or attain a specific value for this cell (Wraith and Or 1998) The location of the variable cell(s) ( e.g parameters in the models) whose value(s) may be altered to achieve the desired target cell ( e.g. RMSE) goal is specified, and constraints may be imposed on any cells involved in the problem Constraints ( e.g. specified ranges for each parameter) take the form of a relationship among a variable, an arithmetic operator ( =, integer), and a constant. s olver provides options to change the maximum time, maximum iterations, precision and tolerance of the iterative optimization. Wraith and Or (1998) indicated that for minimization a user may use a tangent or quadratic approach to obtain the local minimum of basic variables in each iteration. This chapter is divided in five sections. First each model was calibrated for each subject and each condition. Second, a calibration was performed using all the data. Third a calibration considering different traffic conditions was conducted. Fourth, a calibration considering different driver types was performed The last section presents the summary of findings.

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98 Parameter Calibration for Each Subject and Condition Gipps Model This section provides the parameter values after calibration using the optimization tool solver in a spreadsheet program Using previous literature the ranges of constrains were d efined. Gipps (1981) sugges t ed that = (1.7,0. 32 ) m/s2 Based on this, to obtain a 99% confidence level a three standard deviation range was used: = (1.7 30. 32 ) = (1. 43 ,1. 97 ) m/s2 (3. 20 ,4. 41 ) mi /hr -s = 2 m/s2 U sing the computed ranges the ranges are: = 2(1. 43 ,1. 97 ) = ( 2. 86 3. 94 ) m/s2 ( 6. 40, 8. 81 ) mi /hr -s = ( 3,( 3 ) 2 ) m/s2 U sing the computed ranges the ranges are: = (( 2. 86 3) 2 ( 3. 94 3) 2 ) = ( 2. 93 3. 47 ) m/s2 ( 6. 55 7. 76) mi /hr -s Other research papers have suggested different ranges for the Gipps car -following p arameters. For the parameter Wilson (2001) suggest ed 2 (0 mi /hr -s); Panwai and Dia (2005) suggested = 2.5 m/s2 (5.59 mi /hr -s); May (1990) suggested acceleration rates values from 0.89 m/s2 to 1.47 m/s2 (2 mi /hr -s to 3.3 mi /hr -s); and Punzo and Simonelli (2005) suggested = 3.331 m/s2 (7.45 mi /hr -s ), with a variance 4.189. However, Punzo and Simonelli (2005) suggested acceleration rates that were too high in comparison with the other papers. Therefore only the value of 3.331 m/s2 (7.45

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99 mi /hr -s ) was considered in the final selected range. The final range used for the optimization of the speed and spacing RSME are: = [0,3.3] m/s2 [0,7.38] mi /hr -s For the parameter Punzo and Simonelli (2005) suggest ed = 3.801 m/s2 ( 8.50 mi /hr -s), Panwai and Dia (2005) suggested = 4.5 m/s2 (10.06 mi /hr -s), May (1990) suggested values from 1.47 m/s2 to 2.36 m/s2 ( 3.3 mi /hr -s to 5.3 mi /hr -s ), and Ranjitkar et al. (2005) suggested = 3.47 m/s2 ( 7.76 mi /hr -s ), with a standard deviation 0.49. Therefore t he final range used for are: = [ 5, 1.5] m/s2 [ 11.18, 3.35] mi /hr -s For the parameter, Wilson (2001) suggested 2 (0 mi /hr -s ) in congested scenarios Punzo and Simonelli (2005) suggested = 4.783 m/s2 ( 10.69 mi /hr -s) with a variance 10.613 Panwai and Dia (2005) suggested = 8 m/s2 (17.89 mi /hr -s), and Ranjitkar et al. (2005) suggest ed = 4.04 m/s2 ( 9.03 mi /hr -s), with a standard deviation 0.54 Therefore the final range for the parameter used in the optimization is: = [ 8, 2] m/s2 [ 17.9, 4.47] mi /hr -s Tables 6 -1 to 64 present the parameters values after calibration. After calibration for uncongested conditions this is consistent with the findings from Rakha et al. (2007) They indicated that in uncongested conditions speed i s insensitive to traffic flow and density and the speed headway relationship will be linear while the flow -density curve will be an inverted v -shape. The behavior was not considered in this study. Wilson (2001) studied the Gipps car -following model and concluded that behavior produced unrealistic solutions. He indicated behavior produced multiple solutions inside the square root of the equation. Therefore given the unrealistic behavior for such

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100 behavior and that these are not recommended for simulation software this case was not consider in the study. Results show that the Gipps model predicted speed more accurately The RMSE for speed was lower than the RMSE for spacing. Both, in the initial analys is and after calibration Gipps was the second best model in predicting spacing. Table 6-1 to 6-4 presents RMSE values before and after calibration and the parameters values used for each driver in each condition Consistent with the initial analysis the co ndition best predicted by the Gipps model was the rain congested condition. The highest value of RMSE was for uncongested conditions. In uncongested conditions drivers have more flexi bility to increase and decrease their speed. Therefore their behavior in these conditions is difficult to replicate. In addition, t he driver performance best predicted in the initial analysis and after calibration was for the average driver. Pitt Model This section provides the parameter values after calibration using the optim ization tool solver in a spreadsheet program Using previous literature the ranges of constrains were defined. CORSIM default values for (driver sensitivity parameter) vary from 0.35 to 1.25. The value for aggressive driver value is 0.35 and for th e conservative (timid) driver 1.25. Khoury and Hobeika (2006) suggest range from 0.3 to 1.6. The value of (calibration constant) is 0.1 if the follower vehicle speed is highe r than the lead vehicle, zero otherwise. The final intervals used for the optimization were for from 0 to 2 and for from 0 to 0.1. The ranges of were increased more than the suggested ones based on an initial calibration performed by the researcher In this initial calibration

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101 value of from 0.3 to 1.6 were used. When calibrating the model the optimum value for was 0.3 for some subjects. Therefore it was necessary to observ ed if increasing the ranges the optimization parameters values will stay the same as the initial calibration or will change to a new value. Tables of RMSE results before and after calibration are included in Appendix C When calibrating the Pitt model by s pacing 0.10, except for the subject 68 (average driver) which uses the same value of for both calibrations. calibrated by speed has a bigger value that the k calibrated by the spacing, in another words when cal ibrating the spacing the model is assuming a more aggressive driver. This behavior was consistent with values obtained for parameter. W hen calibrating spacing was close to zero, in other words the lead has a higher speed therefore the follower will accelerate or be more aggressive trying to reach their desired speed. The initial analysis showed that the followers speed was the best variable predicted by the Pitt model. After calibration the lowest values of RMSE w ere for the spacing variable. The Pit t model in the initial analysis and after calibration was the model with the highest RMSE for the followers speed. The RMSE for speed decreased from 97.15 to 94.27 but in comparison to the other models has the highest values of RMSE. The Pitt model in the initial analysis and after calibration was the second model predicting better the spacing between vehicles. The Pitt car -following model calculates the spacing variable thus it was expected that this variable was the best predicted After calibration the Pi tt model predicted better congested conditions The worst condition predicted in the initial analysis and after calibration was the uncongested

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102 condition In addition, after calibration the best driver replicated by Pitt was the aggressive and conservative driver. This result is consistent with the initial analysis MITSIM Model This section provides the parameters values after calibration using the optimization tool solver in a spreadsheet program Using previous literature the ranges of constrains were defined. May and Keller (1967) = 2.8; Ozaki (1993) suggested a + = 0.2, + = -= 1 ; Yang and Koutsopoulos (1996) suggested an = 1, however they discussed that for an initial calibration th ese values can be used but they did not performed well. They concluded that the MITSIM parameters should be: + = 0.5, + = 1, + = --= 1 Olstam and Tapani (2004) + = 2.15, + = 1.67, + = -= 1.55, -= 1.65. In addition Punzo and Simonelli (2005) suggested + = 2.512, variance 1.563, + = 0.150, variance 0.099, + = 0.509, variance 0.324 -= 2.328, variance 2.54, -= 0.861, variance 0.485 an = 1.116, variance 0.389. Finally, the MITSIM car -following model parameters ranges used for optimizing the speed and spacing RSME were: + = [0.5, 4] + = [ 2, 1] + = [ 1,3] -= [ 5, 2] -= [0,2] = [ 1,3] Tables of RMSE before and after calibrat ion are included in Appendix C. The MITSIM model is difficult to calibrate b ecause of the larger number of par ameters and degrees of freedom it has. MITSIM utilizes parameters that are not easily interpreted to

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103 known driver or vehicles factors and therefore hard to calibrate (Olstam and Tapani 2004) On the other hand, this amount of parameters and degrees of freedoms make possible the use in dif ferent traffic situations, and capable of reproducing the experimental data better than other models. The MITSIM model predicts the speed variable more accurately. This result was observed also in the initial analysis. The RMSE for speed were lower than th e RMSE for spacing. MITSIM in the initial analysis and after calibration was the model with the lowest value of RMSE for speed and spacing. For all conditions the values of RMSE for spacing and speed was minimized. The MITSIM model predicts best congested conditions and between the congested conditions rainy congested was the best predicted The worst condition predicted in the initial analysis and after calibration for MITSIM was the uncongested. MITSIM initial analysis shows that overall it predicted bet ter the spacing for average drivers and speed for aggressive drivers. After calibration overall the spacing and speed for aggressive drivers was the best driver type predicted by MITSIM. MITSIM overall was the best model replicating the field data after calibration. This can be explained by the numerous parameters that the model has providing a better fit to the field data. Modified Pitt Model This section provides the parameters values after calibration using the optimization tool solver in a spreadsheet program. Cohen (2002) suggested values of from 0.5 to 1. However, the ranges of were increased more than the suggested ones based on an initial calibration performed by the researcher. The final intervals used for the optimization were for from 0 to 2, from 0.5 s to 2 s and fro m 22 ft to 32 ft. (6.7 m to 9.76 m)

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104 Tables of RMSE results before and after calibration are included in Appendix C calibrated by spacing has a bigger value that the calibrated by the speed, in other words when calibrating the spacing the models is assuming a more sensitive driver. The Modified Pitt car -following model is sensitive to the parameter In the initial results the values of RMSE were the highest values, after calibrating this parameter the values of RMSE were lower. values are de fined as a spring constant factor that oscillates depending on the desired FFS and the time to return to an equilibrium condition. Cohen (2002) recommended values of 0. 5 to 1; however this thesis shows that when calibrating this parameter for each driver in each condition the values are much lower. The Modified Pitt model predicted the variable speed more accurately. The Modified Pitt model in the initial analysis presented to be the one of the models with the highest value of RMSE for spacing and spe ed, this behavior was the same after calibration. The RMSE for spacing decreased from 342.14 to 128.11 but in comparison to the other models it has the highest values of RMSE In the initial analysis the best condition predicted by the model was the conges ted condition but after calibration the best was the rain congested condition. The highest RMSE values were for the uncongested condition, similar to the other models. In addition, after calibration the best driver replicated by Modified Pitt was the average driver Summary : Parameters Calibration for Each Model Figure 61 to 6-8 provides comparison graphs of different conditions for the average driver. From this Figures and the results discussed above it can be concluded that all the models generally predi cted more accurately the follower speed. Punzo and

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105 Simonelli (2005) explained that speed deviations and spacing deviations from the field data have a different meaning. They explained that when a model is calibrated on the basis of speed, an error made by the model in calculating the speed between t -1 and t causes an error in the space traveled in the same interval. This is kept equal for all the followings instants where the variable of spacing will increase or decreased by this amount of error in the subsequent instants. They concluded that is easier to fit the models on the basis of speed measurements than the spacing. Based on the calibrations analysis the preferred v ariable for calibrat ing the models was the spacing. Punzo and Simonelli (2005) explained by calibration on the basis of speed, the values of error test calculated for spacing are higher. C alibrating the models for speed will imply a nonneglible error for spacing therefore they suggest spacing as the most reliable measurement of performance. From the Figures 6-1 to 6 8 it can be concluded that comparing between conditions, all the models predicted better the congested conditions than the uncongested scenario. The MITSIM model was the best in predic ting the different conditions. The Second best was the Gipps model, while Pitt was the third best The Modified Pit t model was the most inaccurate of all four models for all conditions. Comparing the models by driver type Pitt predicted overall more accur ately the spacing and MITSIM the speed of conservative and aggressive drivers. MITSIM was the best model predicting average driver behavior. C alibration for Each Model using All Data Calibration was completed using the s olver tool in a spreadsheet progr am After the optimum calibration process describe in the previous section the researcher concluded that the error tests when calibrating the spacing are better that when

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106 calibrating the speed. This result is consistent with previous studies that explained that when calibrating the speed error test for the spacing variable are more sensitive and higher than the optimum ones. When calibrating the spacing or both error test are minimize or the change in error test is not considerably higher that the initial a nalysis. Therefore the calibration using all the field data for each model was done minimizing the sum of the RMSE for spacing. The target cell to minimize was the sum of the spacing RMSE for all drivers in all conditions. The parameter constrains (ranges of values) were the same as those used in the previous section. Results of parameters values for each model and RMSE values before and after calibration are presented in Tables 6-7 to 628. The best model s overall in this analysis predicting the field data w ere the Pitt model for spacing values and the MITSIM model for speed values. Comparing the models by traffic condition, every model fit differently the conditions, however the best condition predicted by all the models was the rain congested condition. O verall for both rainy conditions (congested and uncongested) MITSIM was the best model in predicting the speed and spacing For the congested condition Gipps predicted a more accurately results and for the uncongested condition Pitt predicted a better spacing and MITSIM a better follower speed. Comparing the models by driver type, for conservative and aggressive drivers, the Pitt model predicted a better spacing and MITSIM a better speed. In addition, MITSIM was the best model predicting average driver. Cal ibration by Condition Calibration by traffic condition was completed using the s olver tool in a spreadsheet program. The target cell to minimize was the sum of the spacing RMSE for all drivers in each conditions for each model ( e.g. RMSE for each condition for each

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107 model was calculated and optimize; the different traffic conditions were consider one at the time). The parameter constrains (ranges of values) were the same used as those in the previous section. Results of parameters values for each traffic condition of each model and RMSE values before and after calibration are presented in Tables 629 to 652. The Gipps model results shows that three of the fourth conditions used the same maximum acceleration, only the congested condition has a different val ue. In addition, the absolute values of the deceleration were bigger in the uncongested conditions than the congested. This can be explained based on the interaction of the vehicles in these conditions. In un congested scenarios the vehicles are farther apart and traveling in high speed so the deceleration in case of emergency or sudden stop of the leader resul ts in higher deceleration rate. The Pitt model results shows that t he values of the sensitivity parameter, are a higher value in rain uncongested conditions assuming that the drivers are more conservative in this conditions and more aggressive in the congested conditions. For the Modified Pitt model the values for the congested conditions a re higher than the uncongested. Thi s behavior can be explained in the existence of a higher sensitivity in congested conditions than the uncongested scenarios. Overall the model s predicting more accurately the field data were MITSIM for the spacing variable and Gipps for the speed variable. Comparing the models by traffic condition, it was found that every model fit differently the conditions. However the best condition predicted by all the models was the rain congested condition. For congested conditions Gipps predicted better both

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108 variables For rain uncongested MITSIM was the best model however for rain congested conditions MITSIM predicted a better spacing and Modified Pitt a more accurate speed. For the uncongested conditions Pitt predicted a better spacing and Gipps a more accurately follower speed. Compari ng the models by driver type for conservative drivers, the Pitt model predicted an accurately spacing but Modified Pitt a better follower speed For aggressive drivers, MITSIM was the best model replicating the driver behavior and f or average driver the Gipps model was best for all conditions C alibration by Driver Type Calibration by driver type was completed using the s olver tool in a spreadsheet program The target cell to minimize was the sum of t he spacing RMSE for each driver type in all conditions for each model ( e.g. RMSE for each driver type for each condition and model was calculated and optimize, the different driver types were consider one at the time). The parameter constrains (ranges of values) were the same used as those in the previous se ction. Results of the parameters values for each driver type in each model and RMSE values before and after calibration are presented in Tables 653 to 676. Gipps results shows that t he values of the maximum acceleration were similar for all the drivers, however the deceleration rates were higher for the extreme drivers (conservatives and aggres sive) than the average drivers. For the Pitt model results shows that parameters values for conservative and aggressive drivers are lower than the average drivers. In addition, the Pitt model for this analysis was providing unrealistic results for conservative drivers in rain congested conditions.

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109 The parameters of for the Modified Pitt model were also higher for the average drivers and lower for conservative and aggressive drivers. The values of time headway and length of the vehicle plus a buffer, are lower for aggressive drivers Aggressive drivers tend t o be closer to the lead vehicle therefore this result was expected. Overall t he model that pe rformed the best in this analysis was the MITSIM model for both variables. Comparing the models by condition, every model fit differently the conditions. For congested, and rain congested conditions Gipps predicted an accurate spacing and speed. However, for rain uncongested conditions Pitt were the best predicting the spacing and Gipps the speed The uncongested conditions Pitt predicted a better spacing and MITSIM a more accurate speed Comparing the models by driver type for conservative and aggressive drivers, Pitt predicted a better spacing and MITSIM a better speed. For average driver Gipps predicted more accurate results for both variables Summary of Finding s Calibration is needed for all the models to fit the data accurately. All the models performed better when the parameters where calibrated. MITSIM was the best to fit the field data, and this is caused by the number of parameters that the model has The M ITSIM model predicted the field data more accurately when it was calibrated by driver type. The Pitt model also performed best if the calibration was by driver type. On the other hand, the Modified Pitt model fit the data more accurately if the calibration was by condition. The G ipps model was the only m odel that performed accurately if calibrated by condition or by driver type. The highest values of RMSE for all the models were when calibrating them using all the data.

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110 Three of the four conditions were better predicted if the calibration was done by traffic conditions. The congested condition was better predicted using Gipps and if calibrated by condition. Rain uncongested and rain congested conditions w ere better predicted by MITSIM using the calibration by condition. However the uncongested conditions were better predicted by Pitt (spacing ) and MITSIM (speed ) using the calibration by driver type. For conservative drivers and aggressive drivers the calibration by driver type provided more accurate results. The models that predicted a better trajectory for the conservative and aggressive driver were Pitt for spacing and MITSIM for the follower speed. For average drivers Gipps w as the best model predicting their behavior when calibrating by driver and/or by co ndition. The values of RMSE for both calibrations (driver and condition) using the Gipps model were very similar therefore either one can be used. The Pitt and Gipps models were more accurate when the calibration was done by driver type. The Modified Pitt was best if calibrated by condition. Only the Gipps model show ed accurate results if it was calibrated by driver type or by condition. However when calibrating Gipps by condition the results for the speed variable were more accurate and when calibrated by driver type the results for the sp acing variable were better The differences between the calibrations for the Gipps model were very similar, so either calibration works for Gipps. Overall the calibration by driver type using the MISTIM model was the best and the highest values of RMSE was for the calibration by model

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111 Table 6 -1 Gipps car -following calibration parameters for uncongested conditions Subject number Calibration Parameters R MSE values Spacing Speed 2.00 3.00 3.50 Initial analysis After calibration Initial analysis After calibration 52 Spacing 3.30 5.00 5.00 24.66 10.25 1.75 1.02 Speed 3.30 2.00 2.00 10.73 1.00 72 Spacing 3.30 3.31 3.31 42.79 18.24 2.78 1.40 Speed 3.30 2.00 2.00 67 Spacing 3.30 2.00 2.00 16.42 5.04 1.45 1.22 Speed 3.30 5.00 5.00 5.88 1.21 68 Spacing 2.00 2.49 2.49 8.29 2.62 1.17 0.80 Speed 1.06 3.62 3.62 3.01 0.64 66 Spacing 3.30 5.00 5.03 13.55 3.98 1.69 1.38 Speed 1.19 5.00 5.2 1 6.73 1.05 50 Spacing 3.30 4.56 4.56 45.92 18.69 6.42 5.94 Speed 3.30 4.56 4.56 Table 6 -2 Gipps car -following calibration parameters for congested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial a nalysis After calibration Initial a nalysis After calibration 72 Spacing 2.97 2.00 2.00 2.20 1.34 1.19 1.05 Speed 2.87 2.00 2.00 1.34 1.05 67 Spacing 3.30 2.68 8.00 2.88 1.93 0.72 0. 55 Speed 1.55 1.58 8.00 68 Spacing 2.46 2.72 2.85 1.60 1.26 0.90 0.88 Speed 1.69 2.00 2.00 1.34 0.84 66 Spacing 3.12 2.00 2.00 3.73 1.71 1.14 1.04 Speed 0.83 2.00 2.00 2.99 0.78 50 Spacing 0.34 1.50 2.21 Not w orking for defa ult v alues 23.09 Not w orking for default v alues 2.04 Speed 0.33 1.50 3.92 6.62 0.92 *Using the default values the results were unrealistic.

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112 Table 6 -3 Gipps car -following calibration parameters for rain uncongested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial a nalysis After calibration Initial a nalysis After calibration 52 Spacing 3.30 5.00 5.00 20.60 10.34 2.17 1.77 Speed 2.00 1.50 2.50 49.80 3.43 67 Spacing 1.30 3.66 3.66 5.49 3.67 2.69 2.97 Speed 1.74 4.46 8.00 22.15 2.47 68 Spacing 2.80 5.00 5.03 11.80 2.64 1.54 1.16 Speed 1.27 5.00 5.00 4.36 0.88 50 Spacing 3.30 2.00 2.00 20.81 8.58 1.71 4.94 Speed 2.65 2.00 2.00 8.91 4.94 Table 6 -4 Gipps car -following calibration parameters for rain congested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial a nalysis After calibration Initial a nalysis After calibration 52 Spacing 2.50 2.00 2.00 3.80 2.58 0.79 0.84 Speed 0.33 3.13 3.13 3.59 0.48 67 Spacing 2.00 1.94 2.00 2.17 0.81 0.45 0. 49 Speed 2.00 5.00 5.71 1.32 0.40 68 Spacing 2.00 5.00 5.00 2.99 1.58 0.62 0.60 Speed 2.00 4.81 5.20 2.01 0.59 50 Spacing 3.30 2.00 2.00 3.32 1.47 0.78 0.79 Speed 2.20 2.09 2.33 2.99 0.75

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113 Figure 6-9 After spacing calibration Spacing between lead and follower vehicle for each time interval (u ncongested condition, s ubject 67) Figure 610 After spacing calibration Follower vehicle speed for each time interval (u nc ongested condition, s ubject 67) 0 10 20 30 40 50 60 70 0 5 10 15 20Spacing (meters)Time (sec) Spacing between lead and follower vehicle (uncongested conditions, average driver) Field data Gipps Model Pitt Model MITSIM Model Modified Pitt Model 0 10 20 30 40 50 60 70 0 5 10 15 20Speed (m/s)Time (sec) Follower vehicle speed (uncongested conditions, average driver) Field data Gipps Model Pitt Model MITSIM Model Modified Pitt Model

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114 Figure 611 After spacing calibration Spacing between lead and follower vehicle for each time interval ( c ongested condition, s ubject 67) Figure 612 After s pacing calibration Follower vehicle speed for each time interval (c ongested condition, s ubject 67) 0 10 20 30 40 50 60 70 0 5 10 15 20Spacing (meters)Time (sec) Spacing between lead and follower vehicle (congested conditions, average driver) Field Data Gipps Model Pitt Model MITSIM Model Modified Pitt Model 0 10 20 30 40 50 60 70 0 5 10 15 20Speed (m/s)Time (sec) Follower vehicle speed (congested conditions, average driver) Field Data Gipps Model Pitt Model MITSIM Model Modified Pitt Model

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115 Figure 613 After spacing calibration Spacing between lead and follower vehicle for each time interval ( r ain u ncongested condition, s ubject 67) Figure 614 After spacing calibration Follower vehicle speed for each time interval (r ain u ncongested condition, s ubject 67) 0 10 20 30 40 50 60 70 0 5 10 15 20Spacing (meters)Time (sec) Spacing between lead and follower vehicle (rain uncongested conditions, average driver) Field data Gipps Model Pitt Model MITSIM Model Modified Pitt Model 0 10 20 30 40 50 60 70 0 5 10 15 20Speed (m/s)Time (sec) Follower vehicle speed (rain uncongested conditions, average driver) Field data Gipps Model Pitt Model MITSIM Model Modified Pitt Model

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11 6 Figure 615 After spacing calibration Spacing between lead and follower vehicle for each time interval ( r ain c ongested condition, s ubject 67) Figure 616 After spacing calibration Follower vehicle speed for each time interval (r ain c ongested condition, s ubje ct 67) 0 10 20 30 40 50 60 70 0 5 10 15 20Spacing (meters)Time (sec) Spacing between lead and follower vehicle (rain congested conditions, average driver) Field data Gipps Model Pitt Model MITSIM Model Modiifed Pitt Model 0 10 20 30 40 50 60 70 0 5 10 15 20Speed (m/s)Time (sec) Follower vehicle speed (rain congested conditions, average driver) Field data Gipps Model Pitt Model MITSIM Model Modiifed Pitt Model

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117 Table 6 -5 Calibration using all data Gipps car -following model for uncongested conditions Subject n umber Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial a nalysis After calibration Initial a nalysis After calibration 52 3.30 3.40 3.40 24.66 10.53 1.75 1.01 72 3.30 3.40 3.40 42.79 18.25 2.78 1.41 67 3.30 3.40 3.40 16.42 5.63 1.45 1.22 68 3.30 3.40 3.40 8.29 4.06 1.17 0.97 66 3.30 3.40 3.40 13.55 5.00 1.69 1.54 50 3.30 3.40 3.40 45.92 19.68 6.42 5.94 Total Condition 151.63 63.15 15.25 12.09 Table 6 -6 Calibration using all data Gipps car -following model for congested conditions Subject n umber Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial a nalysis After calibration Initial a nalysis After calibration 72 3.30 3.40 3.40 2.20 1.43 1.19 1.10 67 3.30 3.40 3.40 2.88 3.33 0.72 0.83 68 3.30 3.40 3.40 1.60 1.32 0.90 0.89 66 3.30 3.40 3.40 3.73 2.08 1.14 1.22 50 3.30 3.40 3.40 Not w orking* Not w orking* Using the default values the results were not valid Total c ondition 10.41 8.16 3.95 4.03

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118 Table 6 -7 Calibration using all data Gipps car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial a nalysis After calibration Initial a nalysis After calibration 52 3.30 3.40 3.40 20.60 11.28 2.17 1.76 67 3.30 3.40 3.40 5.49 5.35 2.69 2.87 68 3.30 3.40 3.40 11.80 2.78 1.54 1.28 50 3.3 0 3.40 3.40 20.81 10.31 1.71 1.20 Total c ondition 58.70 29.72 8.11 7.12 Table 6 -8 Calibration using all data Gipps car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial a nalysis After calibration Initial a nalysis After calibration 52 3.30 3.40 3.40 3.80 2.62 0.79 0.87 67 3.30 3.40 3.40 2.17 1.01 0.45 0.48 68 3.30 3.40 3.40 2.99 1.60 0.62 0.61 50 3.30 3.40 3.40 3.32 1.81 0.78 0.80 Total c ondition 12.28 7.04 2.64 2.77 Table 6 -9 Calibration using all data Results by driver type Gipps car -following model R MSE values Spacing Speed Driver type Initial analysis After calibration Initial analysis After calibration Aggressive 94.05 44.11 8.67 6.15 Average 51.63 25.07 9.78 9.16 Conservative 87.34 38.88 11.74 10.70 Table 6 10 Calibration using all data Total RMSE results for the Gipps car -following model Overall RMSE RMSE t otal i nitial RMSE t otal after calibration Spacing Speed Spacing Speed 233.02 29.95 108.07 26.01

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119 Table 6 11 Calibration using all data Pitt car -following model for uncongested conditions Subjec t number Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.00 0.45 4.02 3.06 10.15 10.05 72 0.00 0.45 2.54 3.13 4.88 4.62 67 0.00 0.45 3.96 3.04 6.99 6.76 68 0.00 0.45 15.93 14.42 5.76 5.53 66 0.00 0.45 17.25 15.69 4.36 4.45 50 0.00 0.45 2.94 1.49 2.77 2.76 Total c ondition 46.64 40.83 34.91 34.17 Table 6 12 Calibration using all data Pitt car -following model for congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial a nalysis After calibration Initial a nalysis After calibration 72 0.00 0.45 9.18 6.17 10.36 10.25 67 0.00 0.45 2.91 2.78 2.34 2.25 68 0.00 0.45 3.73 3.73 3.48 3.46 66 0.00 0.45 3.41 3.31 1.68 1.69 50 0.00 0.45 2 .19 2.40 1.25 1.27 Total c ondition 21.42 18.39 19.11 18.91 Table 6 13 Calibration using all data Pitt car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.00 0.45 8.51 6.17 11.08 11.25 67 0.00 0.45 13.52 12.72 9.46 9.85 68 0.00 0.45 14.98 13.74 6.98 6.83 50 0.00 0.45 Not w orking* Not w orking* Total condition 37.01 32.62 27.52 27.92 Using the default values the results were unrealistic

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120 Table 6 14 Calibration using all data Pitt car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.00 0.45 4.06 4.03 5.36 5.26 67 0.00 0.45 1.52 1.06 5.61 5.46 68 0.00 0.45 1.22 1.50 2.74 2.54 50 0.00 0.45 2.69 2.96 1.89 1.89 Total conditio n 9.49 9.55 15.61 15.16 Table 6 15 Calibration using all data Results by driver type Pitt car -following model R MSE v alues Spacing Speed Driver t ype Initial analysis After calibration Initial analysis After calibration Aggressive 28.31 22.55 41.83 41.43 Average 57.78 52.98 43.36 42.68 Conservative 28.48 25.86 10.28 10.37 Table 6 16 Calibration using all data Total RMSE results for the Pitt car -following model Overall RMSE RMSE Total i nitial RMSE t otal a fter calibration Spacing Speed Spacing Speed 114.57 97.15 101.39 96.16

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121 Table 6 17 Calibration using all data MITSIM car -following model for uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.50 1.00 1.00 1.25 1.00 1.00 9.17 9.17 1.05 1.05 72 0.50 1.00 1.00 1.25 1.00 1.00 12.21 12.21 1.20 1.20 67 0. 50 1.00 1.00 1.25 1.00 1.00 6.83 6.83 1.09 1.09 68 0.50 1.00 1.00 1.25 1.00 1.00 6.18 6.18 1.88 1.88 66 0.50 1.00 1.00 1.25 1.00 1.00 6.44 6.44 2.10 2.10 50 0.50 1.00 1.00 1.25 1.00 1.00 14.66 14.66 1.51 1.51 Total condition 55.50 55.50 8 .84 8.84 Table 6 18 Calibration using all data MITSIM car -following model for congested conditions Subject number Parameters RMSE values Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 72 0.50 1.00 1.00 1.25 1.00 1.00 4.62 4.62 1.19 1.19 67 0.50 1.00 1.00 1.25 1.00 1.00 4.71 4.71 0.82 0.82 68 0.50 1.00 1.00 1.25 1.00 1.00 3.54 3.54 0.87 0.87 66 0.50 1.00 1.00 1.25 1.00 1.00 1.67 1.67 0.95 0.95 50 0.50 1.00 1.00 1.25 1.00 1.00 6.77 6.77 1.03 1.03 Total c ondition 21.30 21.30 4.86 4.86

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122 Table 6 19 Calibration using all data MITSIM car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.50 1.00 1.00 1.25 1.00 1.00 10.47 10.47 1.61 1.61 67 0.50 1.00 1.00 1.25 1.00 1.00 4.98 4.98 2.83 2.83 68 0. 50 1.00 1.00 1.25 1.00 1.00 4.62 4.62 1.79 1.79 50 0.50 1.00 1.00 1.25 1.00 1.00 7.14 7.14 1.09 1.09 Total condition 27.21 27.21 7.32 7.32 Table 6 20 Calibration using all data MITSIM car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.50 1.00 1.00 1.25 1.00 1.00 2.21 2.21 0.93 0.93 67 0.50 1.00 1.00 1.25 1.00 1.00 1.34 1.34 0.46 0.46 68 0.50 1.00 1.00 1.25 1.00 1.00 1.28 1.28 0.62 0.62 50 0.50 1.00 1.00 1.25 1.00 1.00 2.85 2.85 0.83 0.83 Total condition 7.70 7.70 2.83 2.83

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123 Table 6 21 Calibration using all data Results by driver type MITSIM car -following model RMSE v alues Driver type Spacing Speed Initial analysis After calibration Initial analysis After calibration Aggressive 38.69 38.69 5.98 5.98 Average 33.49 33.49 10.35 10.35 Conservative 39.53 39.53 6.56 6.56 Table 6 22 Calibration using all data Total RMSE results for the MITSIM car following model Overall RMSE RMSE t otal initial RMSE t otal after calibration Spacing Speed Spacing Speed 111.71 23.85 111.71 23.85 Table 6 23 Calibration using all data Modified Pitt car -following model for uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.12 0.86 22.00 32.80 6.13 8.25 1.28 72 0.12 0.86 22.00 43.15 21.17 10.56 6.39 67 0.12 0.86 22.00 26.62 4.82 6.66 1.28 68 0.12 0.86 22.00 26.78 8.81 7.38 2.12 66 0.12 0.86 22.00 20.84 21.07 7.73 3.34 50 0.12 0.86 22.00 23.95 8.57 7.08 2.47 Total condition 174.14 70.57 47.66 16.89

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124 Table 6 24 Calibration using all data Modified Pitt car -following model for congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial a nalysis After calibration Initial a nalysis After calibration 72 0.12 0.86 22.00 6.34 25.48 3.61 11.66 67 0.12 0.86 22.00 2.04 7.01 0.53 2.54 68 0.12 0.86 22.00 5.17 19.14 1.85 9.16 66 0.12 0.86 2 2.00 10.41 9.76 5.54 2.98 50 0.12 0.86 22.00 4.35 9.37 1.43 3.49 Total c ondition 28.31 70.76 12.96 29.83 Table 6 25 Calibration using all data Modified Pitt car -following model for rain uncongested conditions Subject nu mber Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.12 0.86 22.00 29.49 15.61 8.84 3.74 67 0.12 0.86 22.00 8.13 19.85 3.81 5.63 68 0.12 0.86 22.00 16.81 12.26 5.58 1.82 50 0.12 0.86 22.00 36.23 10.90 9.00 2.33 Total condition 90.66 58.62 27.23 13.51 Table 6 26 Calibration using all data Modified Pitt car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.12 0.86 22.00 10.06 2.94 2.36 0.75 67 0.12 0.86 22.00 9.44 4.29 2.44 1.04 68 0.12 0.86 22.00 10.24 1.86 2.74 0.55 50 0.12 0.86 22.00 13.41 3.10 3.58 0.89 Total c ondition 43.15 12.20 11.12 3.23

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125 Table 6 27 Calibration using all data Results by driver type Modified Pitt car -following model RMSE v alues Driver t ype Spacing Speed Initial a nalysis Aft er c alibration Initial a nalysis After c alibration Aggressive 121.84 71.34 33.62 23.82 Average 105.23 78.04 30.99 24.13 Conservative 109.19 62.77 28.82 12.52 Table 6 28 Calibration using all data Total RMSE results for th e Modified Pitt car following model Overall RMSE RMSE t otal i nitial RMSE t otal after calibration Spacing Speed Spacing Speed 336.26 98.97 212.15 63.46

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126 Table 6 29 Calibration by condition Gipps car -following model for uncongested conditions Subject number Parameters RMSE Values Spacing Speed 2.00 3.00 3.50 Initial Analysis After Calibration Initial Analysis After Calibration 52 3.30 4.56 4.56 24.66 10.32 1.75 1.02 72 3.30 4.56 4.56 42.79 18.47 2.78 1.45 67 3.30 4.56 4.56 16.42 5.84 1.45 1.22 6 8 3.30 4.56 4.56 8.29 4.51 1.17 0.94 66 3.30 4.56 4.56 13.55 4.14 1.69 1.41 50 3.30 4.56 4.56 45.92 18.69 6.42 5.94 Total Condition 151.63 61.98 15.25 11.98 Table 6 30 Calibration by condition Gipps car -followin g model for congested conditions Subject number Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial a nalysis After calibration Initial analysis After calibration 72 2.94 2.00 2.00 2.20 1.34 1.19 1.05 67 2.94 2.00 2.00 2.88 3.26 0.72 0.78 68 2.94 2.00 2.00 1.60 1.30 0.90 0.86 66 2.9 4 2.00 2.00 3.73 1.71 1.14 1.04 50 Not w orking* Not w orking* Using the default values the results were unrealistic Total c ondition 10.41 7.61 3.95 3.72 Table 6 31 Calibration by condition Gipps car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial analysis After calibration Initial analysis After calibration 52 3.30 2.33 2.33 20.60 12.46 2.17 1.77 67 3.30 2.33 2.33 5.49 4.13 2.69 2.88 68 3.30 2.33 2.33 11.80 3.22 1.54 1.35 50 3.30 2.33 2.33 20.81 9.12 1.71 1.12 Total condition 58.70 28.93 8.11 7.12

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127 Table 6 32 Calibration by condition Gipps car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial analysis After calibration Initial analysis After calibration 52 3.30 2.00 2.00 3.80 2.58 0.79 0.84 67 3.30 2.00 2.00 2.17 1.06 0.45 0.51 68 3.30 2.00 2.00 2.99 1.60 0.62 0.64 50 3.30 2.00 -2 .00 3.32 1.47 0.78 0.79 Total condition 12.28 6.71 2.64 2.78 Table 6 33 Calibration by condition Results by driver type Gipps car -following model RMSE v alues Spacing Speed Driver t ype Initial analysis After calibr ation In itial analysis After calibration Aggressive 94.05 45.18 8.67 6.13 Average 51.63 24.92 9.78 9.18 Conservative 87.34 35.13 11.74 10.29 Table 6 34 Calibration by condition Total RMSE r esults for the Gipps car -follow ing model Overall RMSE RMSE t otal i nitial RMSE t otal after calibration Spacing Speed Spacing Speed 233.02 29.95 105.23 25.60

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128 Table 6 35 Calibration by condition Pitt car -following model for uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial analysis After calibration Initial analysis After calibration 52 0.00 0.46 4.02 3.27 10.15 10.00 72 0.00 0.46 2.54 3.39 4.88 4.59 67 0.00 0.46 3.96 2.97 6.99 6.72 68 0.00 0.46 15.93 14.17 5.76 5.50 66 0.00 0.4 6 17.25 15.42 4.36 4.45 50 0.00 0.46 2.94 1.55 2.77 2.75 Total condition 46.64 40.77 34.91 34.01 Table 6 36 Calibration by condition Pitt car -following model for congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial a nalysis After calibration Initial a nalysis After calibration 72 0.00 0.13 9.18 2.80 10.36 10.93 67 0.00 0.13 2.91 3.61 2.34 2.78 68 0.00 0.13 3.73 2.53 3.48 3.60 66 0.00 0.13 3.41 4.32 1.68 1.68 50 0.00 0.13 2.19 1.69 1.25 1.22 Total c ondition 21.42 14.95 19.11 20.22 Table 6 37 Calibration by condition Pitt car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.1 0 0.35 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.00 0.75 8.51 13.75 11.08 9.79 67 0.00 0.75 13.52 10.21 9.46 9.04 68 0.00 0.75 14.98 5.29 6.98 5.68 50 Not w orking* Not w orking* Total c ondition 37.01 29.24 27. 52 24.52 Using the default values the results were unrealistic

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129 Table 6 38 Calibration by condition Pitt car -following model for rain congested conditions Subject number Parameters RMSE Values Spacing Speed 0.10 0.35 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.00 0.38 4.06 3.45 5.36 5.48 67 0.00 0.38 1.52 1.67 5.61 5.63 68 0.00 0.38 1.22 1.17 2.74 2.71 50 0.00 0.38 2.69 2.73 1.89 1.89 Total conditi on 9.49 9.03 15.61 15.71 Table 6 39 Calibration by condition Results by driver type Pitt car following model Driver t ype RMSE v alues Spacing Speed Initial a nalysis After calibration Initial a nalysis After calibration Aggressive 28.31 26.66 41.83 40.79 Average 57.78 41.61 43.36 41.67 Conservative 28.48 25.71 10.28 10.32 Table 6 40 Calibration by condition Total RMSE r esults for the Pitt car -following model Overall RMSE RMSE t otal i ni tial RMSE t otal after calibration Spacing Speed Spacing Speed 114.57 97.15 93.99 94.45

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130 Table 6 41 Calibration by condition MITSIM car -following model for uncongested conditions Subject number Parameters RMSE Values Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 52 0.96 0.90 0.88 0.55 0.00 0.26 9.17 6.64 1.05 1.37 72 0.96 0.90 0.88 0.55 0.00 0.26 12.21 7.95 1.20 1.31 67 0.9 6 0.90 0.88 0.55 0.00 0.26 6.83 4.57 1.09 1.77 68 0.96 0.90 0.88 0.55 0.00 0.26 6.18 10.14 1.88 3.50 66 0.96 0.90 0.88 0.55 0.00 0.26 6.44 6.48 2.10 6.45 50 0.96 0.90 0.88 0.55 0.00 0.26 14.66 11.36 1.51 2.01 Total condition 55.50 47.15 8.84 16.42 Table 6 42 Calibration by condition MITSIM car -following model for congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial a nalysis After calibration Initial a nalysis After calibration 72 0.50 1.00 1.00 1.25 1.00 1.00 4.62 4.62 1.19 1.19 67 0.50 1.00 1.00 1.25 1.00 1.00 4.71 4.71 0.82 0.82 68 0.50 1.00 1.00 1.25 1.00 1.00 3.54 3.54 0.87 0.87 66 0.50 1.00 1.00 1.25 1.00 1.00 1.67 1.67 0.95 0.95 50 0.50 1.00 1.00 1.25 1.00 1.00 6.77 6.77 1.03 1.03 Total condition 21.30 21.30 4.86 4.86

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131 Table 6 43 Calibration by condition MITSIM car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 52 4.00 1.00 2.16 0.58 2.00 2.31 10.47 4.32 1.61 1.05 67 4.00 1.00 2.16 0.58 2.00 2.31 4.98 5.76 2.83 2.56 68 4.00 1. 00 2.16 0.58 2.00 2.31 4.62 3.29 1.79 0.38 50 4.00 1.00 2.16 0.58 2.00 2.31 7.14 2.98 1.09 1.01 Total condition 27.21 16.35 7.32 4.99 Table 6 44 Calibration by condition MITSIM car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.67 1.00 1.00 1.31 1.15 1.00 2.21 2.50 0.93 1.26 67 0.67 1.00 1.00 1.31 1.15 1.00 1.34 0.78 0.46 0.70 68 0.67 1.00 1.00 1.31 1.15 1.00 1.28 1.28 0.62 0.73 50 0.67 1.00 1.00 1.31 1.15 1.00 2.85 2.14 0.83 0.97 Total condition 7.70 6.70 2.83 3.66

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132 Table 6 45 Calibration by condition Results by driver type MITSIM car -following model RMSE v alues Driver type Spacing Speed Initial analysis After calibration Initial analysis After calibration Aggressive 38.69 26.03 5.98 6.18 Average 33.49 34.07 10.35 11.34 Conservative 39.53 31.39 6.56 11.47 Table 6 46 Calibration by condition Total RMSE r esults for the MITSIM car -following model Overall RMSE RMSE t otal i nitial RMSE t otal a fter calibration Spacing Speed Spacing Speed 111.71 23.85 91.50 29.94 Table 6 47 Calibration by condition Modified Pitt car -following model for uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial a nalysis After calibration Initial a nalysis After calibration 52 0.16 0.72 22.00 32.80 5.15 8.25 1.98 72 0.16 0.72 22.00 43.15 22.06 10.56 6.17 67 0.16 0.72 22.00 26.62 2.80 6.66 1.02 68 0.16 0.72 22.00 26.78 4.46 7.38 1.69 66 0.16 0.72 22.00 20.84 20.97 7.73 4.01 50 0.16 0.72 22.00 23.95 3.54 7.08 1.32 Total condition 174.14 58.97 47.66 16.20 Table 6 48 Calibration by condition Modified Pitt car -following mode l for congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial analysis After calibration Initial analysis After calibration 72 0.45 1.91 22.00 6.34 5.20 3.61 3.73 67 0.45 1.91 22.00 2.04 2.21 0.53 0.89 68 0.45 1.91 22.00 5.17 3.83 1.85 1.73 66 0.45 1.91 22.0 0 10.41 6.42 5.54 2.42 50 0.45 1.91 22.00 4.35 3.23 1.43 2.30 Total c ondition 28.31 20.88 12.96 11.07

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133 Table 6 49 Calibration by condition Modified Pitt car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial analysis After calibration Initial analysis After calibration 52 0.07 1.10 22.00 29.49 9.11 8.84 2.10 67 0.07 1.10 22.00 8.13 18.20 3.81 3.55 68 0.07 1.10 22.00 16.81 4.12 5.58 1.00 50 0.07 1.10 2 2.00 36.23 18.40 9.00 1.25 Total Condition 90.66 49.83 27.23 7.90 Table 6 50 Calibration by condition Modified Pitt car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial analysis After calibration Initial analysis After calibration 52 0.18 0.93 22.00 10.06 2.04 2.36 0.72 67 0.18 0.93 22.00 9.44 2.62 2.44 0.85 68 0.18 0.93 22.00 10.24 1.85 2.74 0.60 50 0.18 0.93 22.00 13.41 2.64 3.58 0.58 Total Condition 43.15 9.16 11.12 2.76 Table 6 51 Calibration by condition Results by driver type Modified Pitt car -following model RMSE v alues Driver t ype Spacing Speed Initial analysis After calibrati on Initial analysis After calibration Aggressive 121.84 43.57 33.62 14.71 Average 105.23 40.08 30.99 11.34 Conservative 109.19 55.20 28.82 9.47 Table 6 52 Calibration by condition Total RMSE r esults for the Modified Pi tt car following model Overall RMSE RMSE t otal i nitial RMSE t otal a fter calibration Spacing Speed Spacing Speed 336.26 98.97 138.85 37.93

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134 Table 6 53 Calibration by driver type Gipps car -following model for uncongested c onditions Subject number Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial analysis After calibration Initial analysis After calibration 52 3.30 5.00 5.00 24.66 10.25 1.75 1.02 72 3.30 5.00 5.00 42.79 18.51 2.78 1.47 67 3.11 2.19 2.19 16.42 5.23 1.45 1.23 68 3 .11 2.19 2.19 8.29 3.37 1.17 1.00 66 3.30 4.44 4.44 13.55 4.20 1.69 1.42 50 3.30 4.44 4.44 45.92 18.77 6.42 5.94 Total c ondition 151.63 60.33 15.25 12.08 Table 6 54 Calibration by driver type Gipps car -following model for congested conditions Subject number Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial analysis After calibration Initial analysis After calibration 72 3.30 5.00 5.00 2.20 1.51 1.19 1.15 67 3.11 2.19 2.19 2.88 3.27 0.72 0.79 68 3.11 2.19 2.19 1.60 1.30 0.90 0.86 66 3.30 4.44 4.44 3.73 2.32 1.14 1.33 50 Not w orking* Not w orking* Total c ondition 10.41 8.40 3.95 4.13

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135 Table 6 55 Calibration by driver type Gipps car -following model for rain uncongested conditions Subject numbe r Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial analysis After calibration Initial analysis After calibration 52 3.30 5.00 5.00 20.60 10.34 2.17 1.77 67 3.11 2.19 2.19 5.49 4.03 2.69 2.88 68 3.11 2.19 2.19 11.80 3.53 1.54 1.36 50 3.3 0 4.44 4.44 20.81 10.98 1.71 1.28 Total c ondition 58.70 28.88 8.11 7.30 Table 6 56 Calibration by driver type Gipps car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 2.00 3.00 3.50 Initial analysis After calibration Initial analysis After calibration 52 3.30 5.00 5.00 3.80 2.68 0.79 0.93 67 3.11 2.19 2.19 2.17 1.05 0.45 0.50 68 3.11 2.19 2.19 2.99 1.60 0.62 0.63 50 3.30 4.44 4.44 3.32 2.01 0.78 0.85 Total condition 12.28 7.34 2.64 2.91 Table 6 57 Calibration by driver type Results by driver type Gipps car -following model RMSE v alues Spacing Speed Driver t ype Initial analysis After calibrati on Initial analysis After calibration Aggressive 94.05 43.28 8.67 6.34 Average 51.63 23.39 9.78 9.26 Conservative 87.34 38.28 11.74 10.82 Table 6 58 Calibration by driver type Total RMSE r esults for the Gipps car -follo wing model Overall RMSE RMSE t otal i nitial RMSE t otal a fter calibration Spacing Speed Spacing Speed 233.02 29.95 104.95 26.42

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136 Table 6 59 Calibration by driver type Pitt car -following model for uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial analysis After calibration Initial analysis After calibration 52 0.00 0.36 4.02 2.84 10.15 10.52 72 0.00 0.36 2.54 2.15 4.88 4.92 67 0.00 0.70 3.96 6.78 6.99 5.79 68 0.00 0.70 15.93 8.28 5.76 4.63 66 0.10 0.47 17.25 13.68 4.36 4.30 50 0.10 0.47 2.94 1.99 2.77 2.67 Total condition 46.64 35.72 34.91 32.83 Table 6 60 Calibration by driver type Pitt car -following model for congested conditions Subject number Parameters RMSE Valu es Spacing Speed 0.10 0.35 Initial analysis After calibration Initial analysis After calibration 72 0.00 0.36 9.18 5.07 10.36 10.44 67 0.00 0.70 2.91 2.99 2.34 1.87 68 0.00 0.70 3.73 4.63 3.48 3.38 66 0.10 0.47 3.41 3.35 1.68 1.69 50 0.10 0.47 2.19 2.51 1.25 1.26 Total condition 21.42 18.55 19.11 18.65 Table 6 61 Calibration by driver type Pitt car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0 .10 0.35 Initial analysis After calibration Initial analysis After calibration 52 0.00 0.36 8.51 4.77 11.08 11.67 67 0.00 0.70 13.52 10.36 9.46 9.18 68 0.00 0.70 14.98 6.65 6.98 5.89 50 0.10 0.47 Not w orking* Not w orking* Total c ondition 37.01 2 1.78 27.52 26.74 Using the default values the results were unrealistic

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137 Table 6 62 Calibration by driver type Pitt car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial analysis After calibration Initial analysis After calibration 52 0.00 0.36 4.06 3.29 5.36 5.55 67 0.00 0.70 1.52 3.53 5.61 4.79 68 0.00 0.70 1.22 3.66 2.74 1.91 50 0.10 0.47 2.69 3.16 1.89 1.89 Total c onditi on 9.49 13.64 15.61 14.14 Table 6 63 Calibration by driver type Results by driver type Pitt car -following model RMSE v alues Spacing Speed Driver type Initial analysis After calibration Initial analysis After calibrati on Aggressive 28.31 18.12 41.83 43.10 Average 57.78 46.88 43.36 37.44 Conservative 28.48 24.69 10.28 10.13 Table 6 64 Calibration by driver type Total RMSE r esults for the Pitt car -following model Overall RMSE RMSE t otal i nitial RMSE t otal a fter calibration Spacing Speed Spacing Speed 114.57 97.15 89.69 92.35

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138 Table 6 65 Calibration by driver type MITSIM car -following model for uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 52 0.50 0.81 0.84 1.20 0.69 1.13 9.17 3.34 1.05 0.52 72 0.50 0.81 0.84 1.20 0.69 1.13 12.21 4.30 1.20 0.75 67 0.5 0 1.55 1.00 2.00 0.00 0.65 6.83 4.71 1.09 0.61 68 0.50 1.55 1.00 2.00 0.00 0.65 6.18 2.33 1.88 0.38 66 0.50 0.85 0.93 1.19 0.13 0.30 6.44 10.95 2.10 2.27 50 0.50 0.85 0.93 1.19 0.13 0.30 14.66 7.26 1.51 1.12 Total c ondition 55.50 32.88 8. 84 5.65 Table 6 66 Calibration by driver type MITSIM car -following model for congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initi al analysis After calibration 72 0.50 0.81 0.84 1.20 0.69 1.13 4.62 6.26 1.19 1.40 67 0.50 1.55 1.00 2.00 0.00 0.65 4.71 2.66 0.82 0.55 68 0.50 1.55 1.00 2.00 0.00 0.65 3.54 3.01 0.87 0.98 66 0.50 0.85 0.93 1.19 0.13 0.30 1.67 1.96 0.95 0.94 50 0.50 0.85 0.93 1.19 0.13 0.30 6.77 4.27 1.03 1.01 Total condition 21.30 18.16 4.86 4.88

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139 Table 6 67 Calibration by driver type MITSIM car -following model for rain uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 52 0.50 0.81 0.84 1.20 0.69 1.13 10.47 4.61 1.61 1.10 67 0.50 1.55 1.00 2.00 0.00 0.65 4.98 3.31 2.83 2.41 68 0.5 0 1.55 1.00 2.00 0.00 0.65 4.62 3.54 1.79 0.41 50 0.50 0.85 0.93 1.19 0.13 0.30 7.14 2.16 1.09 0.89 Total condition 27.21 13.63 7.32 4.81 Table 6 68 Calibration by driver type MITSIM car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 52 0.50 0.81 0.84 1.20 0.69 1.13 2.21 4.76 0.93 0.84 67 0.50 1.55 1.00 2.00 0.00 0.65 1.34 3.11 0.46 0.35 68 0.50 1.55 1.00 2.00 0.00 0.65 1.28 2.82 0.62 0.58 50 0.50 0.85 0.93 1.19 0.13 0.30 2.85 4.73 0.83 0.86 Total condition 7.70 15.42 2.83 2.62

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140 Table 6 69 Calibration by driver type Results by driver type MITSIM car -f ollowing model RMSE v alues Driver t ype Spacing Speed Initial analysis After calibration Initial analysis After calibration Aggressive 38.69 23.25 5.98 4.60 Average 33.49 25.49 10.35 6.27 Conservative 39.53 31.34 6.56 6.15 Table 6 70 Calibration by driver type Total RMSE r esults for the MITSIM car following model Overall RMSE RMSE t otal i nitial RMSE t otal a fter calibration Spacing Speed Spacing Speed 111.71 23.85 80.08 17.96 Table 6 71 Calibration by driver type Modified Pitt car -following model for uncongested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial analysis After calibration Initial analysis After calibration 52 0.12 0.78 25.61 32.80 5.37 8.25 1.22 72 0.12 0.78 25.61 43.15 20.88 10.56 6.47 67 0.21 0.89 32.00 26.62 13.02 6.66 4.50 68 0.21 0.8 9 32.00 26.78 12.57 7.38 4.05 66 0.16 0.67 24.07 20.84 21.48 7.73 4.16 50 0.16 0.67 24.07 23.95 3.49 7.08 1.25 Total c ondition 174.14 76.79 47.66 21.66 Table 6 72 Calibration by driver type Modified Pitt car -following model for congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial analysis After calibration Initial analysis After calibration 72 0.12 0.78 25.61 6.34 25.81 3.61 12.47 67 0.21 0.89 32.00 2.04 4.21 0.53 2.20 68 0.21 0.89 32.00 5.17 14.09 1.85 8.40 66 0.16 0.67 2 4.07 10.41 8.23 5.54 4.07 50 0.16 0.67 24.07 4.35 9.11 1.43 6.11 Total condition 28.31 61.46 12.96 33.24

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141 Table 6 73 Calibration by driver type Modified Pitt car -following model for rain uncongested conditions Subject n umber Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial analysis After calibration Initial analysis After calibration 52 0.12 0.78 25.61 29.49 16.09 8.84 4.15 67 0.21 0.89 32.00 8.13 15.73 3.81 4.93 68 0.21 0.89 32.00 16.81 8.80 5.58 2.62 50 0.16 0.67 24.07 36.23 12.40 9.00 3.34 Total c ondition 90.66 53.02 27.23 15.05 Table 6 74 Calibration by driver type Modified Pitt car -following model for rain congested conditions Subject number Parameters RMSE v alues Spacing Speed 0.35 1.50 32.00 Initial analysis After calibration Initial analysis After calibration 52 0.12 0.78 25.61 10.06 2.68 2.36 0.69 67 0.21 0.89 32.00 9.44 1.49 2.44 0.36 68 0.21 0.89 32.00 10.24 5.19 2.74 1.87 50 0.16 0.67 24.07 1 3.41 2.73 3.58 0.85 Total condition 43.15 12.09 11.12 3.76 Table 6 75 Calibration by driver type Results by driver type Modified Pitt car following model RMSE v alues Driver type Spacing Speed Initial analysis After calibration Initial analysis After calibration Aggressive 121.84 70.82 33.62 25.00 Average 105.23 75.09 30.99 28.92 Conservative 109.19 57.45 28.82 15.71 Table 6 76 Calibration by driver type Total RMSE r esults for the Modified Pitt car following model Overall RMSE RMSE t otal i nitial RMSE t otal a fter calibration Spacing Speed Spacing Speed 336.26 98.97 203.37 73.71

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142 CHAPTER 7 CONCLUSIONS AND RECO MMENDATIONS The accuracy of computer simulation programs used to devel op transportation systems depends on the quality of the traffic -flow models from which they are derived. T he three main components of this traffic -flow models are car -following lane changing and gap acceptance models. This study evaluates car -following F our models were selected based o n their application in existing simulation programs and in the differences between them. Field data w ere obtained from a database consisting of data collected in Jacksonville, Florida. The data w ere collected by an instrumented vehicle recording speed, time and distances between the subject vehicle and its leader. The data captured critical factors such as human characteristics, different conditions (congested and uncongested) for different time s of day and different environ mental conditions (rain). The investigation methodology used is described in Chapter 3. T he car -following behavior for each model was compared to field data using a number of error tests. The error test root mean square error (RMSE) was used on spacing and speed as a key performance indicator. Results show : The v ariable predicted be st by the models was the speed of the following vehicle The RMSE for speed was low er than the spacing for all the conditions for all the drivers for all the analysis. This is co nsistent with previous studies which explained that in comparison to the spacing, the speed does not increas e or decrease accumulatively E rror in predicting it does not accumulate every second. The calibration results show that the best variable to calibrate is the spacing. This is consistent with previous studies that explained that if calibrating on speed, the values of RMSE calculated for spacing are going to be higher and more sensitive than the optimum ones the re will be higher values o f error obtai ned than calibrating the model by spacing.

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143 Results of the MITSIM model present the lowest values of RMSE for the initial analysis using the default values MITSIM is capable of reproducing the field data better than the other models. However this performance can be due to the large number of parameters and degrees of freedom that may tend to over fit the data. C ongested scenarios were the conditions most accurate predicted by all the models. Results in some cases are mixed. The model that predicted more precisely the congested conditions w as Gipps for the initial analysis and MITSIM for the calibration analysis. On the other hand uncongested scenarios were better predicted by MITSIM for the initial analysis and for the calibration analysis. For the initial analysis the performance of average drivers was better predicted by all models. The model s that predicted average driver behavior the best w ere MITSIM and Gipps, before and after calibration. C onservative and aggressive driver s were the highest values of RMSE in the initial analysis H owever the Pitt model predicted their spacing and MITSIM their speed more accurately After calibration Pitt predicted better the conservative behavior and MITSIM the aggressive. The calibration analysis shows that the conge sted conditions are better predicted when the parameters are calibrated by condition U ncongested conditions were better predicted when the parameters are calibrated by driver type. The calibration analysis shows that for conservative and aggressive driver s behavior is better predicted when calibrated by driver type A verage driver s behavior is better predicted when the parameters were calibrated by driver or condition depending on its condition. The average driver from the initial analysis was predicted accurately T herefore it does not need to be calibrated It already works for all the models. It is recommended to use the following parameter ranges for the car -following models if conservative and aggressive driver behaviors are to be analyzed. Gipps mod el: Aggressive driver = 3.3 m/s2 (7.38 mi /hr -s) = -5.0 m/s2 (-11.18 mi /hr s), = -5.0 m/s2 (-11.18 mi /hr -s) Average driver, = 3.11 m/s2 (6.96 mi /hr -s), = 2.19 m/s2 (-4.9 mi /hr -s) = -2.19 m/s2 (4.9 mi /hr -s) Co nservative driver, = 3.3 m/s2 (7.38 mi /hr -s), = 4.44 m /s2 (-9.93 mi /hr s), = -4.44 m/s2 (9.93 mi /hr -s)

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144 Pitt model: Aggressive = 0.0 and = 0.36 Average driver, = 0.0 and = 0.70 Conservative driver, = 0.10 and = 0. 47 MITSIM model: Aggressive + = 0.5, + =0.81, + =--= 1.13 Average driver + = 0.5, + = 1.55, + = --= 0.65 Conservative driver + = 0.5, + = -0.85, + = ---= 0.13, and = 0.3 Modified Pitt model: Aggressive driver = 0. 12, = 0.78, = 25.61 ft (7.81 m) Average driver, = 0. 21, = 0.89, = 32 ft (9.76 m) Conservative driver, = 0. 16, = 0.67, = 24.07 ft (7.34 m) T he lowest values of RMSE w ere when the parameters of Gipps were calibrated by condition and driver type. It is recommended to use or either the above mentioned parameters or the following parameters ranges for the car -following models Modified Pitt has the lowest RMSE when the parameters were by condition. Therefore the following parameters are recommended. Gipps model: Uncongested conditions = 3.3 m/s2 (7.38 mi /hr -s), = -4.56 m/s2 (9.95 mi /hr -s) = 4.56 m/s2 (-9.95 mi /hr -s). Congested conditions = 2.94 m/s2 ( 6.58 mi /hr -s), = -2.0 m/s2 (-4.47 mi /hr -s) = 2.0 m/s2 (4.47 mi /hr -s) Rain uncongested cond itions = 3.3 m/s2 (7.38 mi /hr -s), = 2.33 m/s2 (5.21 mi /hr -s) = 2.33 m/s2 (-5.21 mi /hr -s) R ain congested conditions = 3.3 m/s2 (7.38 mi /hr -s), = -2.0 m/s2 (-4.47 mi /hr -s), = 2.0m/s2 (4.47 mi /hr -s) Modified Pitt model: Uncongested conditions = 0. 16, = 0.72, = 22 ft (6.71 m) Congested conditions = 0. 45, = 1.91, = 22 ft (6.71 m) Rain uncongested conditions = 0. 07, = 1.10, = 22 ft (6.71 m)

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145 Rain congested conditions, = 0 .1 8, = 0.93, = 22 ft (6.71 m) The lowest values of RMSE f or Pitt and MITSIM were when the parameters were calibrated by driver type However the values of RMSE overall were lowest when ca librating the parameter values by driver type using the MITS IM model. MITSIM was the best model in incorporating all the different conditions and drivers. In conclusion, this thesis recommends performed calibration using spacing and to conduct c alibration by driver type It is recommended to use the parameter range s for calibration by driver type for each car -following model M odifications to various simulation programs allowing more flexibility in setting car following parameters related to different traffic conditions and drivers types is recommended. This study shows that different drivers types affect the performance of the car -following models T herefore different drivers have to be consider ed in the car following models of simulation programs. Research on the implementation of these findings in the micro -sim ulations software has to be undertaken. T his study only considered car -following behavior. I n future studies other important factors such as lane changing behavior and gap acceptance should be considered. The distance s between vehicles (subject/follower and the lead) are estimated for each consecutive frame using the method applied for measuring distances from still images explained by Psarianos et al. ( 2001) An instrumented vehicle with infrared sensor will provide more accurately measures of distances. This thesis is based on Jacksonville, Florida field data; therefore additional data collection in various locations is needed to confirm and refine the find ings.

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146 APPENDIX A PROCEDURE USED TO OB TAINED SPEED AND LEN GHT MEASUREMENTS The method used to obtained measurements of length and speed from the cameras is described in this section. Is necessary to understand the trajectories and record the different spee d of the subjects for comparisons with the outputs of the equations models. Procedures use on Psarianos et al (2001) research paper was implemented to extract the data from the cameras installed on the Pilot car. For this thesis the front camera is the only that will be evaluated. The basic geometry of lane width measurement is shown in Figure A1, in which O d enotes the perspective center and M is the image center. The X axis in object space and the x image coordinate axis are normal to the plane of the Figure. Figure A -1 Image acquisition geometry with camera axis horizontal (l eft) and tilted (right) (Psarianos et al. 2001) On the left, the situation is illustrated when the camera axis is horizontal. The camera constant is denoted by while is the y image coordinates of points B and B on the road surface defining lane width. If 0 is the camera height above ground level, then image scale at the distance is expressed as follows: = 0 = (A-1) Where:

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147 is the lane width BB is the co rrespondin g length measured on the image. The method to estimate the values is by using the vanishing point of the direction of depth, found graphically on the frame. One can define the vanishing point F of a straight road segment by exploiting road delineation on the video snapshots, as shown in Figure A-2. Figure A -2 Graphical determination of vanishing points The formula used to connect a lane width measured on the image (at a certain y image coordinate) through the vanishing point F of the road direction with the Equation A-2. = 0 (A-2)

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148 Figure A -3 Measurements on the digital camera Psarianos et all (2001) In addition, the lane widths shown on these frames had been measured with a tape and were later used to estimate camera height 0. This value of 0 does not represent the actual camera height but is affected by image affin ity. Figure A -4 Images of the process for estimating the 0 and Before employing the described approach on a routine basis, its accuracy was evaluated. To this end, 4 frames were first used to estimate a camera height 0 from known widths. Here, the lane widths had been measured by tape to serve for checking purposes. On each of these 30 frames, 5 different measurements were taken at different y levels on the image plane, as illustrated in Figure A-4, and c orresponding ground lane widths were computed. All five measurements from each frame were

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149 averaged to produce the absolute mean difference from the known value. The difference (s) from the known width was also computed. The final result is the calibration parameter that will be used to compute the distances between the follower vehicle and his l ead.

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150 APPENDIX B RESULTS OF INITIAL ANALYSIS This section provides ta bles with detail results of each driver in each condition by model. Each model is subdivided by condition and by driver. The tables provided the ma ximum differences between the results of the models and the field data in terms of distances, speed and RMSE. Table B -1 Gipps results for each driver in uncongested and congested conditions Subject number Uncongested condition Congested condition RMSE v alues Max d ifference RMSE v alues Max d ifference Spacing Speed Spacing Speed Sp acing Speed Spacing Speed Initial a nalysis Initial a nalysis 52 24.66 1.75 33.53 m (109.98 ft) 3.99 m/s (8.92 mi/hr) ** ** ** ** 72 42.79 2.78 58.13 m (190.66 ft) 4.53 m/s (10.13mi/hr) 2.20 1.19 5.67 m (18.60 ft) 2.62 m/s (5.85mi/hr) 67 16.42 1.45 21.58 m (70.78 ft) 2.82 m/s (6.30 mi/hr) 2.88 0.72 9.96 m (32.67 ft) 2.27 m/s (5.07mi/hr) 68 8.29 1.17 14.32 m (49.97 ft) 2.73 m/s (6.11 mi/hr) 1.60 0.90 3.32 m (10.89 ft) 2.17 m/s (4.85mi/hr) 66 13.55 1.69 24.93 m (81.77 ft) 3.86 m/s (8.63 mi/hr) 3.7 3 1.14 6.68 m (21.91 ft) 3.76 m/s (8.40mi/hr) 50 45.92 6.42 63.38 m (207.88 ft) 5.61 m/s (12.55mi/hr) * Using default values results were unrealistic ** Subject did not drive in that traffic condition

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151 Table B -2 Gipps results for each driver in rainy uncongested and congested conditions Subject number Rain uncongested condition Rain congested condition RMSE v alues Max d ifference RMSE v alues Max d ifference Spacing Speed Spacing Speed Spacing Speed S pacing Speed Initial a nalysis Initial a nalysis 52 20.60 2.17 27.24 m (90.98 ft) 5.83 m/s (13.04mi/hr) 3.80 0.79 7.41 m (24.30 ft) 1.74 m/s (3.89mi/hr) 72 ** ** ** ** ** ** ** ** 67 5.49 2.69 18.57 m (60.91 ft) 4.97 m/s (11.11mi/hr) 2.17 0.45 3.9 2 m (12.86 ft) 1.16 m/s (2.59mi/hr) 68 11.80 1.54 21.53 m (70.62 ft) 3.20 m/s (7.16 mi/hr) 2.99 0.62 4.98 m (16.33 ft) 1.68 m/s (3.76mi/hr) 66 ** ** ** ** ** ** ** ** 50 20.81 1.71 27.65 m (90.69 ft) 5.13 m/s (11.47mi/hr) 3.32 0.78 5.36 m (17.58 ft) 2.4 7 m/s (5.52mi/hr) Using default values results were unrealistic ** Subject did not drive in th at traffic condition Table B -3 Pitt results for each driver in uncongested and congested conditions Subject number Unc ongested condition Congested condition RMSE v alues Max d ifference RMSE v alues Max d ifference Spacing Speed Spacing Speed Spacing Speed Spacing Speed Initial a nalysis Initial a nalysis 52 4.02 10.15 7.8 m (25.5 ft) 12.07m/s (27mi/hr) ** ** ** ** 72 2.54 4.88 4.4m (14.4 ft) 7.5m/s (16.7mi/hr) 9.18 10.36 15.1 m (49.54 ft) 14.62 m/s (32.7 mi/hr) 67 3.96 6.99 8.4 m (28 ft) 9.28 m/s (21 mi/hr) 2.91 2.34 10.3 m (33.8 ft) 2.88 m/s (6.44mi/hr) 68 15.93 5.76 24.33 m (79.8 ft) 7.35m/s (16.44mi/hr) 3.73 3.48 7.9 m (25.91 ft) 6.21 m/s (13.89 mi/hr) 66 17.25 4.36 25.88 m (85 ft) 6.57 m/s (15 mi/hr) 3.41 1.68 6.91 m (22.7 ft) 3.47 m/s (7.76mi/hr) 50 2.94 1.97 6.73 m (22ft) 4.35 m/s (9.7mi/hr) 2.19 1.25 3.57 m(11.7 ft) 3.26 m/s (7.29 mi/hr) Using default values results were unrealistic ** Subject did not drive in th at traffic condition

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152 Table B -4 Pitt results for each driver in rainy uncongested and congested conditions Subject number Rain uncongested condition R ain congested condition RMSE v alues Max difference RMSE v alues Max difference Spacing Speed Spacing Speed Spacing Speed Spacing Speed Initial analysis Initial analysis 52 8.51 11.08 15.5 m (50.85 ft) 14.11m/s (31.6mi/hr) 4.06 5.36 8.4 m (2 6.8 ft) 6.56 m/s (14.7 mi/hr) 72 ** ** ** ** ** ** ** ** 67 13.52 9.46 25.8 m (84.64 ft) 10.61m/s (23.7mi/hr) 1.52 5.61 3.7m (13.02 ft) 7.03m/s (15.73mi/hr) 68 14.98 6.98 20.2 m (66 ft) 8.56m/s (19.15mi/hr) 1.22 2.74 2.2 m (7.22 ft) 3.43 m/s (7.67 mi/hr ) 66 ** ** ** ** ** ** ** ** 50 * 2.69 1.89 5.09 m (17 ft) 3.13m/s (7mi/hr) Using default values results were unrealistic ** Subject did not drive in th at traffic condition Table B -5 MITSIM results for e ach driver in uncongested and congested conditions Subject number Uncongested condition Congested condition RMSE v alues Max difference RMSE v alues Max difference Spacing Speed Spacing Speed Spacing Speed Spacing Speed Initial analysis Initial analy s is 52 9.17 1.05 13.2 m (43 ft) 2.34m/s (5.23mi/hr) ** ** ** ** 72 12.21 1.20 18.8m (62 ft) 2.5m/s (6mi/hr) 4.62 1.19 7.4 m (24.3 ft) 2.42 m/s (5.41 mi/hr) 67 6.83 1.09 10.4 m (30.12ft) 2.7 m/s (6.04 mi/hr) 4.71 0.82 13.3 m (43.6 ft) 2.47 m/s (5.52m i/hr) 68 6.18 1.88 11.9 m (39.04ft) 3.98m/s (9mi/hr) 3.54 0.87 5.1 m (16.7 ft) 1.91 m/s (4.3 mi/hr) 66 6.44 2.10 13.1 m (43 ft) 4.71 m/s (10.5 mi/hr) 1.67 0.95 4.5m (14.7 ft) 2.23 m/s (5mi/hr) 50 14.66 1.51 19.9 m (65ft) 4.46 m/s (10mi/hr) 6.77 1.03 10. 7 m (35.1 ft) 3.02 m/s (6.8 mi/hr) Using default values results were unrealistic ** Subject did not drive in that traffic condition

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153 Table B -6 MITSIM results for each driver in rainy uncongested and congested conditions Subject number Rain uncongested condition Rain congested condition RMSE v alues Max difference RMSE v alues Max difference Spacing Speed Spacing Speed Spacing Speed Spacing Speed Initial analysis Initial analysis 52 10.47 1.61 15.7 m (51.5 ft) 4.63m/s (10.4mi/hr) 2.21 0.93 4.3m (14.10 ft) 3.05 m/s (6.82 mi/hr) 72 ** ** ** ** ** ** ** ** 67 4.98 2.83 9.4m (30.8 ft) 4.70m/s (10.5mi/hr) 1.34 0.46 3.5m (11.4 ft) 1.15m/s (2.57mi/hr) 68 4.62 1.79 9.1m (30ft) 4.32m/s (9.7mi/hr) 1.28 0.62 2.7m (8.9ft) 1.6 m/s (3.6 mi/hr) 66 ** ** ** ** ** ** ** ** 50 7.14 1.09 11.3 m (37 ft) 3.38 m/s (7.6 mi/hr) 2.85 0.83 5.9 m (19.4 ft) 2.32m/s (5.2mi/hr) Using default values results were unrealistic ** Subject did not drive in that traffic con dition Table B -7 Modified Pitt results for each driver in uncongested and congested conditions Subject number Uncongested condition Congested condition RMSE v alues Max difference RMSE v alues Max difference Spacing Sp eed Spacing Speed Spacing Speed Spacing Speed Initial analysis Initial analysis 52 32.80 8.25 57.06 m (187.2ft) 12.9m/s (28.85mi/hr) ** ** ** ** 72 43.15 10.56 70.54m (231.4ft) 14.98m/s (33.5mi/hr) 6.34 3.61 20.48m (67.17ft) 6.80 m/s (15.21mi//hr) 67 24.53 6. 83 44.35m (145.5ft) 10.34m/s (23 mi/hr) 2.04 0.53 5.84 m (19.15ft) 0.87 m/s (1.95mi/hr) 68 26.78 7.38 51.37 m (168.5ft) 11.48 m/s (25.67mi/hr) 5.17 1.85 12.53m (41.10 ft) 2.43 m/s (5.43 mi/hr) 66 20.84 7.73 38.38 m (125.9ft) 12.27m/s (27.44m i/hr) 10.41 5.54 17.98 m (58.97ft) 3.74 m/s (7.67 mi/hr) 50 23.95 7.08 42.58 m (139.7ft) 12.52 m/s (27.99mi/hr) 4.35 1.43 14.53 m (47.66 ft) 2.43 m/s (5.43 mi/hr) Using default values results were unrealistic ** Subject did not drive in th at traff ic condition

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154 Table B -8 Modified Pitt results for each driver in rainy uncongested and congested conditions Subject number Rain uncongested condition Rain congested condition RMSE v alues Max difference RMSE v alues Max diff erence Spacing Speed Spacing Speed Spacing Speed Spacing Speed Initial analysis Initial analysis 52 29.49 8.84 56.46 m (134.5 ft) 15.38 m/s (34.39mi/hr) 10.06 2.36 17.49 m (57.36 ft) 4.42 m/s (9.88 mi/hr) 72 ** ** ** ** ** ** ** ** 6 7 8.13 3.81 17.83 m (58.48 ft) 4.0m/s (8.94 mi/hr) 9.44 2.44 17.05 m (55.92 ft) 3.90 m/s (9.88 mi/hr) 68 16.81 5.58 33.31 m (109.2 ft) 8.19m/s (18.32mi/hr) 10.24 2.74 17.78 m (58.32 ft) 4.19 m/s (9.37 mi/hr) 66 ** ** ** ** ** ** ** ** 50 36.23 9.00 59.78 m (196.1 ft) 13.35 m/s (29.9 mi/hr) 13.41 3.58 23.95 m (78.56 ft) 5.27 m/s (11.8 mi/hr) Using default values results were unrealistic ** Subject did not drive in that traffic condition

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155 APPENDIX C PARAMETERS VALUES AFTER CALIBRATION Car -following models calibration parameters for each driver by each condition are presented in this section. Table C-1 Pitt car -following calibration parameters for uncongested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial analysis After calibration Initial analysis After calibration 52 Spacing 0.00 0.40 4.02 2.48 10.15 10.32 Speed 0.10 1.70 32.49 0.56 72 Spacing 0.00 0.38 2.54 2.03 4.88 4.85 Speed 0.10 1.27 27.50 2.21 67 Spacing 0.00 0.48 3.96 2.90 6.99 6.64 Speed 0.10 1.55 23.39 0.62 68 Spacing 0.10 0.93 15.93 4.02 5.76 3.61 Speed 0.10 1.57 12.52 0.35 66 Spacing 0.03 0.96 17.25 3.72 4.36 4.26 Speed 0.10 2.00 33.44 3.56 50 Spacing 0.00 0.44 2.94 1.49 2.77 2.76 Speed 0.10 2.00 47.19 1.63 Table C -2 Pitt car -following calibration parameters for congested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial analysis After ca libration Initial analysis After calibration 72 Spacing 0.00 0.07 9.18 2.64 10.36 11.06 Speed 0.00 2.00 16.66 4.36 67 Spacing 0.00 0.49 2.91 2.77 2.34 2.18 Speed 0.10 1.81 5.57 0.35 68 Spacing 0.10 0.00 3.73 2.11 3.48 3.68 Speed 0.10 0.85 5.60 3.36 66 Spacing 0.00 0.44 3.41 3.31 1.68 1.69 Speed 0.10 0.00 5.15 1.68 50 Spacing 0.10 0.00 2.19 1.51 1.25 1.21 Speed 0.10 0.00

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156 Table C -3 Pitt car -following calibration parameters for rain uncongested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial analysis After calibration Initial analysis After calibration 52 Spacing 0.00 0.31 8.51 4.52 11.08 11.91 Speed 0.10 1.87 28.97 1.34 67 Spacing 0.00 0.79 13.52 10.18 9.46 8.95 Speed 0.10 2.00 22.15 3.75 68 Spacing 0.04 0.89 14.98 2.51 6.98 5.05 Speed 0.00 1.77 18.09 0.24 50 Spacing Not working for d efault Values Can't calibrate Not working for d efault Values Can't calibrate Speed Table C -4 Pitt car -following calibration parameters for rain congested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.10 0.35 Initial analysis After calibration Initial analysis After calibration 52 Spacing 0.00 0.22 4.06 2.70 5.36 6.03 Speed 0.10 1.85 13.45 0.57 67 Spacing 0.00 0.47 1.52 1.01 5.61 5.40 Speed 0.10 1.72 12.36 0.20 68 S pacing 0.00 0.36 1.22 1.15 2.74 2.76 Speed 0.10 1.22 7.13 0.38 50 Spacing 0.10 0.33 2.69 2.68 1.89 1.89 Speed 0.10 0.35 2.69 1.89

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157 Table C -5 MITSIM car -following calibration parameters for uncongested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 52 Spacing 1.79 0.09 0.11 1.58 0.00 0.05 9.17 0.77 1.05 6.94 Speed 0.50 2.00 1.15 0.00 0.00 0.91 3.24 0.34 72 Spacing 0.59 0.75 1.00 1.25 0.92 1.10 12.21 0.99 1.20 1.04 Speed 4.00 1.36 1.00 1.74 2.00 3.00 5.14 0.53 67 Spacing 0.50 1.12 1.00 2.00 2.00 2.52 6.83 2.21 1.09 0.53 Speed 0.50 1.16 1.00 2.00 2.00 2.76 3.61 0.47 68 Spacing 0.53 0.99 -1 .00 1.26 1.11 0.94 6.18 2.06 1.88 4.03 Speed 2.94 1.04 2.03 0.33 0.00 2.91 3.62 0.25 66 Spacing 0.50 1.00 0.21 1.01 0.96 1.24 6.44 3.35 2.10 0.45 Speed 0.50 2.00 3.00 0.54 0.35 0.77 3.44 0.34 50 Spacing 0.60 0.85 1.00 1.21 0.81 1.15 14.66 2. 60 1.51 0.84 Speed 4.00 1.49 1.00 0.36 2.00 3.00 6.48 0.48 Table C -6 MITSIM car -following calibration parameters for congested conditions Subject number Calibration Parameters RMSE v alues Spacing S peed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 72 Spacing 0.50 0.26 0.25 2.00 0.03 0.11 4.62 0.72 1.19 1.21 Speed 4.00 0.32 0.79 2.00 0.25 0.46 3.75 1.08 67 Spacing 4.00 2.00 0.24 0.00 2.00 1.00 4.71 1.73 0.82 0.43 Speed 4.00 2.00 3.00 5.00 0.00 1.30 1.77 0.33 68 Spacing 0.50 0.06 0.17 2.00 0.00 0.45 3.54 1.33 0.87 0.86 Speed 0.88 0.96 0.82 1.68 0.00 0.56 4.61 0.81 66 Spacing 0.50 1.00 0.72 2.00 0.00 0.25 1.67 1.54 0.95 0.99 Speed 1.26 1.00 1.37 0.14 0.00 3.00 6.20 0.86 50 Spacing 0.50 1.02 0.99 2.00 2.00 0.99 6.77 3.76 1.03 1.15 Speed 0.60 2.00 1.00 2.00 2.00 0.60 4.39 1.07

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158 Table C -7 MITSIM car -following calibration parameters for rain uncongested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 52 Spacing 2.01 0.63 0.55 2.00 0.78 0.92 10.47 1.05 1.61 6.22 Speed 0.60 0.52 0.10 0.09 0.00 0.28 4.03 0.94 67 Spacing 1.44 1.28 0.57 0.25 0.00 0.02 4.98 3.03 2.83 2.47 Speed 1.03 1.00 2.00 0.09 1.62 2.00 8.12 1.88 68 Spacing 0.68 1.00 1.00 1.45 1.30 1.15 4.62 2.07 1.79 5.64 Speed 0.50 2.00 3.00 0.00 0.00 1.00 2.99 0.22 50 Spacing 0.50 0.78 1.00 2.00 2.00 2.52 7.14 1.81 1.09 0.87 Speed 1.55 0.24 0.03 1.89 2.00 2.89 4.93 0.81 Table C -8 MITSIM car -following calibration parameters for rain congested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.50 1.00 1.00 1.25 1.00 1.00 Initial analysis After calibration Initial analysis After calibration 52 Spacing 3.17 1.00 2.07 0.55 0.46 2.99 2.21 1.32 0.93 0.58 Speed 4.00 1.00 1.92 1.98 2.00 3.00 2.24 0.41 67 Spa cing 1.75 0.21 0.20 2.00 0.00 0.01 1.34 0.49 0.46 1.17 Speed 0.50 2.00 1.23 0.00 2.00 1.00 1.30 0.23 68 Spacing 1.19 1.00 1.26 0.35 0.00 3.00 1.28 1.13 0.62 0.45 Speed 0.65 0.18 0.31 0.53 0.00 3.00 1.21 0.45 50 Spacing 4.00 0.40 0.98 2.00 2.00 1.80 2.85 1.21 0.83 1.08 Speed 0.50 0.36 0.26 2.00 2.00 2.27 3.17 0.69

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159 Table C -9 Modified Pitt car -following calibration parameters for uncongested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.35 1.50 32 ft Initial analysis After calibration Initial analysis After calibration 52 Spacing 0.15 0.76 22.00 32.80 4.46 8.25 1.42 Speed 0.00 2.00 32.00 5.08 0.34 72 Spacing 0.41 1.16 22.00 43.15 32.53 10.56 14.57 Speed 0.00 1.92 32.00 65.58 4.38 67 Spacing 0.13 0.73 22.00 24.53 1. 11 6. 83 0. 56 Speed 0.00 2.00 32.00 2.76 0.61 68 Spacing 0.02 0.50 22.00 26.78 2.77 7.38 1.38 Speed 0.03 0.90 22.00 11.39 0.80 66 Spacing 0.40 0.85 22.00 20.84 13.47 7.73 6. 52 Speed 0.00 1.52 32.00 9.25 0.88 50 Spacing 0.16 0.70 22.00 23.95 3.34 7.08 1.12 Speed 0.16 0.51 32.00 4.57 0.69 Table C -10 Modified Pitt car -following calibration parameters for congested conditions Subject numbe r Calibration Parameters RMSE v alues Spacing Speed 0.35 1.50 32 ft Initial analysis After calibration Initial analysis After calibration 72 Spacing 0.35 1.42 22.00 9.47 7.40 3.53 3.49 Speed 0.23 1.68 32.00 12.66 2.49 67 Spa cing 0.46 1.57 22.00 3.83 1.95 0.41 0.69 Speed 0.42 1.56 28.75 3.09 0.35 68 Spacing 0.53 1.24 22.00 7.71 3.00 0.99 1.02 Speed 0.39 1.13 30.85 4.99 0.50 66 Spacing 0.20 0.61 22.00 12.13 3.31 2.14 1.35 Speed 0.27 1.34 22.00 7.77 1.09 50 Spacing 0.55 2.00 22.00 6.05 4.63 1.69 1.67 Speed 0.48 2.00 23.43 4.84 1.62

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160 Table C -11 Modified Pitt car -following calibration parameters for rain uncongested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.35 1.50 32 ft Initial analysis After calibration Initial analysis After calibration 52 Spacing 0.28 0.61 28.92 24.49 4.10 8.84 1.43 Speed 0.01 2.00 32.00 6.18 1.03 67 Spacing 0.71 1.63 22.00 8.13 6.51 3.81 3.93 Speed 0.07 1.68 22.00 8.37 2.57 68 Spacing 0.27 1.07 22.00 16.81 8.02 5.58 2.82 Speed 0.20 1.05 22.00 8.38 2.07 50 Spacing 0.39 1.03 22.00 36.23 25.81 9.00 12.35 Speed 0.09 0.75 22.00 8.50 0.82 Table C -12 Modifi ed Pitt car -following calibration parameters for rain congested conditions Subject number Calibration Parameters RMSE v alues Spacing Speed 0.35 1.50 32 ft Initial analysis After calibration Initial analysis After calibration 52 Spacing 0.01 0.50 22.00 10.06 2.32 2.36 0.59 Speed 0.20 1.04 22.00 2.22 0.62 67 Spacing 0.02 2.00 32.00 9.44 0.46 2.44 0.19 S peed 0.02 2.00 32.00 0.51 0.19 68 Spacing 0.18 0.79 22.00 10.24 0.51 2.74 0.37 Speed 0.12 0.69 22.00 0.95 0.26 50 Spacing 0.14 0.51 32.00 13.41 1.81 3.58 0.52 Speed 0.14 0.53 32.00 1.87 0.50

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161 LIST OF REFERENCES Ahn, S., Cassidy, M. J., and Laval, J. (2004). Verification of a simplified car -following theory. Transportation Research Part B: Methodological 38(5), 431440. Bham, G. H., and Benekohal, R. F. (2004). A high fidelity traffic simulation model based on cellular automata and car -following concepts. Transportation Research Part C: Emerging Technologies 12(1), 1-32. Brackstone, M., and McDonald, M. (1999). Car -following: A historical review. Transportation Research Part F: Traffic Psychology and Behavior 2(4) 181-196. Chakroborty, P., and Kikuchi, S. (1999). Evaluation of the General Motors based car following models and a proposed fuzzy inference model. Transportation Research Part C: Emerging Technologies 7(4), 209235. Chandler, R. E., Herman, R., and Montroll, E. W. (1958). Traffic d ynamics: Studies in c ar -following. Operations Research, 6(2), 165-184. Chundury, S., and Wolshon, B. (2000). Evaluation of CORSIM c ar -Following m odel by u sing Global Positioning System f ield d ata. Transportation Research Record: Journal of the Transportation Research Board, 1710( 1), 114-121. Cohen, S. (2002). Application of c ar -f ollowing s ystems in m icroscopic t ime-s can s imulation m odels. Transportation Research Record: Journal of the Transportation Research Board, 1802( -1), 239 -247. Edie, L. C. (1961). Car -f ollowing and s teady -s tate t heory for n oncongested t raffic. Operations Research, 9(1), 6676. Fritzsche, H. T. (1994). A model for traffic simulation. Traffic Engineering Control 35, 317 321. Gazis, D. C., Herman, R., and Potts, R. B. (1959). Car -f ollowing t heory of s teady -s tate t raffic f low. Operations Research, 7(4), 499 -505. Gazis, D. C., Herman, R., and Rothery, R. W. (1961). Nonlinear f ollow -t he -l eader m odels of t raffic f low. Operations Research 9(4), 5 45567. Gipps, P. (1981). A behavioral car -following model for computer simulation. Transportation Research Part B: Methodological Transportation Research Part B: Methodological, 15(2), 105 -111. Herman, R., Montroll, E. W., Potts, R. B., and Rothery, R. W. (1959). Traffic d ynamics: a nalysis of s tability in c ar -f ollowing Operations Research, 7(1), 86106.

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162 Khoury, J. E., and Hobeika, A. (2006). Simulation of an ITS Crash p revention t echnology at a no-p assing z one s ite. Journal of Intelligent Transpo rtation Systems: Technology, Planning, and Operations 10(2), 75. Kim, T., Lovell, D., and Park, Y. (2007). Empirical a nalysis of u nderlying m echanisms and v ariability in c ar -f ollowing b ehavior. Transportation Research Record: Journal of the Transportation Research Board, 1999( 1), 170179. Kondyli, A. (2009). Breakdown p robability m odel at f reeway -ramp m erges b ased on d river b ehavior University of Florida, Gainesville, Fla. Lownes, N. E., and Machemehl, R. B. (2006). VISSIM: a multi -parameter sensitivi ty analysis. Proceedings of the 38th conference on Winter simulation Winter Simulation Conference, Monterey, California, 1406-1413. May, A. D. (1990). Traffic flow fundamentals Prentice Hall. May, A. D., and Keller, H. E. (1967). Noninteger car -follow ing models. Highway Research Board, 19 32. Newell, G. F. (1961). Nonlinear e ffects in the d ynamics of c ar -f ollowing. Operations Research, 9(2), 209-229. Olstam, J., and Tapani, A. (2004). Comparison of c ar -following models Department of Science and Technology (ITN), Campus Norrk \ ping, Link \ ping University [Institutionen f \ r teknik och naturvetenskap (ITN), Campus Norrk \ ping, Link \ pings universitet]. Ozaki, H. (1993). Reaction and anticipation in the car -following behavior. Proceedings of the 13th International Symposium on Traffic and Transportation Theory 366. Panwai, S., and Dia, H. (2005). Comparative evaluation of microscopic car -following behavior. IEEE Transactions on Intelligent Transportation Systems 6(3), 314 325. Pindyck, R. S., and Rubinfeld, D. L. (n.d.). Econometric m odels and e conomic f orecasts. 1998. McGraw -Hill Book Co., New York, NY. Psarianos, B., Paradissis, D., Nakos, B., and Karras, G. E. (2001). A cost effective road surveying method for the assessment of road alignments. IV International Symposium Turkish -German Joint Geodetic Days 3 6. Punzo, V., and Simonelli, F. (2005). Analysis and c omparison of m icroscopic t raffic f low m odels with r eal t raffic m icroscopic d ata. Transportation Research Record: Journal of the Transportation Research Board, 1934( 1), 53-63. Rakha, H., Eng, P., and Gao, Y. (2010). Calibration of s teady -state c ar -following m odels using m acroscopic l oop d etector d ata. TRB 2010 Annual Meeting CD -ROM

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163 Rakha, H., Pecker, C., and Cybis, H. (2007). Calibr ation p rocedure for Gipps c ar f ollowing m odel. Transportation Research Record: Journal of the Transportation Research Board, 1999( -1), 115 -127. Ranjitkar, P., Nakatsuji, T., and Kawamura, A. (2005). Experimental a nalysis of c ar f ollowing d ynamics and t raffic s tability. Transportation Research Record: Journal of the Transportation Research Board, 1934( 1), 22-32. Treiterer, J., and MYERS, J. A. (1974). The hysteresis phenomenon in traffic flow. Transportation and Traffic Theory: Proceedings of the Six th International Symposium on Transportation and Traffic Theory, University of New South Wales, Sydney, Australia, 2628 August 1974 13. Wiedemann, R., and Reiter, U. (1992). Microscopic t raffic s imulation, t he s imulation s ystem m ission. Background and Actual State, CEC Project ICARUS (V1052) Final Report Wilson, R. E. (2001). An analysis of Gipps's car -following model of highway traffic. IMA J Appl Math, 66(5), 509 -537. Wraith, J. M., and Or, D. (1998). Nonlinear parameter estimation using spreadshe et software. Journal of Natural Resources and Life Sciences Education 27, 13 19. Yang, Q., and Koutsopoulos, H. N. (1996). A m icroscopic t raffic s imulator for evaluation of dynamic traffic management systems. Transportation Research Part C: Emerging Te chnologies 4(3), 113129. Zhang, H. M., and Kim, T. (2005). A car -following theory for multiphase vehicular traffic flow. Transportation Research Part B 39(5), 385 399.

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164 BIOGRAPHICAL SKETCH Irene Soria was born i n 1985 in San Juan Puerto Rico. The o ldest daughter she grew up mostly in Bayamon Puerto Rico, graduating from Academia Santa Teresita in 2002. She earned her B.S. in c ivil e ngineering from the University of Puerto Rico (Mayaguez Campus) in 2008 In the f all of 2007, she participated in a n undergraduate research p rogram called UPR/PURP/ATI, researching in the collective transport of Puerto Rico. In addition, she was a teacher assistan t for the introductory course of trans portation and traffic engineering to 113 civil engineering students Ir ene succesfully completed the Fundamentals of Engineering (FE) examination in 2008. Irene received her Master of Engineering in civil engineering from the University of Florida in the spring of 2010. S he was enrolled in the t ransportation e ngineering progr am. Her specific research interest is in traffic flow theory, driver behavior and geometric design. She center ed her research and thesis on the enhancement of car following models. She also serve d as a graduate research and teacher assistant at the Univers ity of Florida Irene has know ledge in different simulations programs like AIM SUN, CORSIM, Synchro, Passer, and Transyt 7-F. As well she knows programs such as AutoCad, EPANET, Eagle Point, SAP, SPSS, SAS and Nlogit. She has been a recipient of the Dwight Eisenhower Fellowship where she had the opportunity to accomplish an intership at the University of Rhode Island. She is a member of Tau Beta Pi a honor society for engineer s Institu te of Transportation Engineers and the American Society of Civil En gineers Upon completion of her master s program she plans to seek a position in a civil engineering firm or government agency