| Figure 1. |
Formula. Relationship between inputs, outputs, and model parameters |
| Figure 2. |
Formula. Fitness functions used as the objective function in calibration |
| Figure 3. |
Formula. Weather effect coefficient in DYNASMART-P |
| Figure 4. |
Diagram. Schematic representation of different conditions that impact a transportation network |
| Figure 5. |
Formula. State-space formulation for generic online calibration |
| Figure 6. |
Formula. Relationship between time mean speed and space mean speed |
| Figure 7. |
Flowchart. The traffic analysis tools calibration procedure |
| Figure 8. |
Formula. Relationship between density and space mean speed |
| Figure 9. |
Formula. Space mean speed in the two-fluid theory |
| Figure 10. |
Formula. Relationship between road density and fraction of stopped vehicles |
| Figure 11. |
Formula. Density as a function of velocity and acceleration |
| Figure 12. |
Illustration. Parameters with the least level of uncertainty [type 1] |
| Figure 13. |
Illustration. Parameters with some level of uncertainty [type 2] |
| Figure 14. |
Formula. Regret formulation |
| Figure 15. |
Illustration. Parameters with the deep uncertainty [type 3] |
| Figure 16. |
Flowchart. Overall framework |
| Figure 17. |
Illustration. Process of developing a scenario/agent |
| Figure 18. |
Flowchart. Proposed calibration framework |
| Figure 19. |
Illustration. Constructing model output (travel time) distribution based on scenario-specific simulation outputs |
| Figure 20. |
Formula. Newell car-following model (trajectory translation model) |
| Figure 21. |
Formula. Gipps car-following model |
| Figure 22. |
Formula. Helly car-following model |
| Figure 23. |
Formula. The Intelligent Driver Model |
| Figure 24. |
Formula. The stimulus-response acceleration model in MITSIMLab |
| Figure 25. |
Formula. The Lane-Changing Model with Relaxation and Synchronization |
| Figure 26. |
Formula. A probabilistic model for lane changing |
| Figure 27. |
Formula. A gap acceptance model based on standard cumulative normal distribution |
| Figure 28. |
Formula. A probit gap acceptance model for bicyclists and motorists |
| Figure 29. |
Formula. Queue discharge rate in DYNASMART-P |
| Figure 30. |
Graph. Type 1 modified Greenshields model (dual-regime model) |
| Figure 31. |
Formula. Type 1 modified Greenshields model |
| Figure 32. |
Graph. Type 2 modified Greenshields model (single-regime model) |
| Figure 33. |
Formula. Type 2 modified Greenshields model |
| Figure 34. |
Formula. Greenberg’s logarithmic model |
| Figure 35. |
Formula. Underwood’s exponential model |
| Figure 36. |
Formula. Pipes’ generalized model |
| Figure 37. |
Formula. Weather effect adjustment of model parameters in DYNASMART |
| Figure 38. |
Formula. Weather adjustment factor as a function of weather condition |
| Figure 39. |
Formula. Scheduling cost in a demand model proposed by Frei et al. (2014) |
| Figure 40. |
Formula. Link-level cost function proposed by Perez et al. (2012) |
| Figure 41. |
Formula. A generalized mode choice utility function |
| Figure 42. |
Formula. A time-of-day choice utility function |
| Figure 43. |
Formula. A destination choice utility function |
| Figure 44. |
Formula. Highway utility function proposed by Vovsha et al. (2013) |
| Figure 45. |
Flowchart. Entity relationship diagram of the model parameter libraries |
| Figure 46. |
Illustration. Process of generating agents and scenarios |
| Figure 47. |
Flowchart. Scenario-based analysis |
| Figure 48. |
Flowchart. Robustness-based analysis |
| Figure 49. |
Illustration. I-290E study segment in Chicago, IL |
| Figure 50. |
Formula. Value function for the uncongested regime |
| Figure 51. |
Formula. Value function for the congested regime |
| Figure 52. |
Formula. Binary probabilistic regime selection model |
| Figure 53. |
Formula. Total utility function for the choice of acceleration |
| Figure 54. |
Formula. Probability density function for the evaluation of drivers’ stochastic response |
| Figure 55. |
Formula. The intelligent driver acceleration model |
| Figure 56. |
Illustration. Radar sensor formation on an automated vehicle |
| Figure 57. |
Formula. Maximum speed of automated vehicles |
| Figure 58. |
Formula. Acceleration model for automated vehicles |
| Figure 59. |
Diagram. Maximum safe speed curve |
| Figure 60. |
Formula. Safe following distance formula |
| Figure 61. |
Formula. Acceleration of automated vehicles |
| Figure 62. |
Chart. Extended form of the lane-changing game with inactive vehicle-to-vehicle communication |
| Figure 63. |
Diagrams. Compound figure depicts fundamental diagrams for different demand levels |
| Figure 64. |
Equation. Weighted average travel time of the scenarios |
| Figure 65. |
Charts. Compound figure depicts travel time distribution for mainline vehicles under different interarrival time scenarios |
| Figure 66. |
Charts. Compound figure depicts fundamental diagrams for different levels of aggressiveness in driving behavior |
| Figure 67. |
Charts. Compound figure depicts travel time distributions for mainline vehicles under different aggressive driving scenarios |
| Figure 68. |
Diagram. Fundamental diagrams for different levels of aggressiveness in driving behavior |
| Figure 69. |
Charts. Compound figure depicts travel time distribution for the mainline vehicles under various aggressive driver and conservative driver mix scenarios |
| Figure 70. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 0 percent and the automated vehicle market penetration rate is 0 percent |
| Figure 71. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 0 percent and the automated vehicle market penetration rate is 25 percent |
| Figure 72. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 0 percent and the automated vehicle market penetration rate is 50 percent |
| Figure 73. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 0 percent and the automated vehicle market penetration rate is 75 percent |
| Figure 74. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 0 percent and the automated vehicle market penetration rate is 100 percent |
| Figure 75. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 25 percent and the automated vehicle market penetration rate is 0 percent |
| Figure 76. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 25 percent and the automated vehicle market penetration rate is 25 percent |
| Figure 77. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 25 percent and the automated vehicle market penetration rate is 50 percent |
| Figure 78. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 25 percent and the automated vehicle market penetration rate is 75 percent |
| Figure 79. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 50 percent and the automated vehicle market penetration rate is 0 percent |
| Figure 80. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 50 percent and the automated vehicle market penetration rate is 25 percent |
| Figure 81. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 50 percent and the automated vehicle market penetration rate is 50 percent |
| Figure 82. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 75 percent and the automated vehicle market penetration rate is 0 percent |
| Figure 83. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 75 percent and the automated vehicle market penetration rate is 25 percent |
| Figure 84. |
Charts. Compound figure depicts fundamental diagrams for a scenario in which the connected vehicle market penetration rate is 100 percent and the automated vehicle market penetration rate is 0 percent |
| Figure 85. |
Equation. Travel time based on the Hurwicz optimism pessimism rule |
| Figure 86. |
Diagram. Fundamental diagrams of mixed traffic scenarios |
| Figure 87. |
Diagrams. Compound figure depicts average travel time at different market penetration rates for autonomous vehicles and connected vehicles on a selected segment of I-290 |
| Figure 88. |
Diagram. Example for calculating the regret summation for the speed in the speed-density profile |
| Figure 89. |
Diagram. Regret-based robustness metrics for different performance measures |
| Figure 90. |
Diagram. Scenario rankings for various regret-based robustness metrics and performance measures |
| Figure 91. |
Formula. Multivariate kernel density estimation formula |
| Figure 92. |
Illustration. Compound figure depicts the process of smoothing the simulation output using the multivariate kernel density estimation method |
| Figure 93. |
Formula. Relative mean integrated square error |
| Figure 94. |
Formula. Minimum number of simulation runs for each scenario |
| Figure 95. |
Formula. Bayes’ rule |
| Figure 96. |
Formula. Relationship between prior and posterior states of mutually exclusive scenarios |
| Figure 97. |
Formula. Revised Bayes’ rule |
| Figure 98. |
Equation. Relationship between prior and posterior probabilities in example 1 |
| Figure 99. |
Equation. Relationship between prior and posterior probabilities in example 2 |
