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 |