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Subject Index
AHS,361
Algorithm, 74
bisection, 76
diagonalization/relaxation, 80, 125, 154
DYNAS'rOCH1,184 DYNASTOCH2,188
Frank-Wolfe, 77, 125, 154
golden section, 76
penalty, 152
Arrival time choice, 210, 293
bonus or penalty for early or late arrival, 210
Arterial links, 344
Artificial, 126
origins, 126
links, 127
Assignment
all-or-nothing, 124 incremental, 126 logit-based flow-independent
route, 185, 189
ATIS,3
ATMS,3
AVI,329
Backward pass, 184, 189
Bilevel programs, 47
for departure time/route choice, 208
follower problem, 45
leader problem, 45
lower level problem, 209, 231
optimal control, 47, 211, 231
upper level problem, 211, 233
Bang-Bang control, 31
BPR function, 341
Bonus/penalty, 210
Boundary conditions, 23
Capacity, 93
Complementarity problem, 71
Compliance of drivers, 173
Congestion pricing, 359
various strategies, 328
toll based instantaneous DUO, 331
toll based ideal DUO, 333
Control, 5
feedback, 22
total, 5
partial, 6
variables, 18, 83
Constraints, 83
equilibrating actual route travel times, 145
378
for departure time/route choice, 211,293
for departure time/mode/route choice, 234
for discrete ideal SDUO route choice, 196
for discrete instantaneous route choice, 120
for discrete instantaneous SDUO route choice, 193
for DSO route choice, 315
for ideal route choice, 141, 143, 149, 269, 273
for ideal SDUO route choice, 173, 175,177
for instantaneous route choice, 103, 245, 251
for instantaneous SDUO route choice, 165
for mean actual route travel times, 175
Convex combination (see FrankWolfe algorithm)
Convergence test, 125
Costate equation, 215
Cray, 134
Cumulative number of vehicles, 85
entering, 88
exiting, 85, 88
arriving, 142
departing, 142
Data, 362
O-D matrices, 362
network geometry, 353
traffic flow, 354
travel characteristics, 354
Decision node, 101, 172
Decompose, 123
Definitions of travel times, 86, 163
deterministic, 86
perceived, 163
Delay function, 343
queuing delay, 345
stop delay, 345
Subject Index
uniform delay, 345
oversaturation delay, 345
Departure flow pattern, 219
initial, 219
improved, 219
Departure time choice, 209
bilevel program, 207
two-stage model, 234
variational inequality, 291
DSO route choice, 321
route choice controller, 208
departure time coordinator, 208
waiting time, 209
driving time, 209
desired arrival time interval, 209
Departure time/route choice, 205
Departure time/mode/route choice, 225
stratification of travelers, 227
two-stage model, 227
time interval and time period, 227
highway network, 229
transit network, 229
first stage, 230
second stage, 231
operating cost, 232, 250
Dispersed route choice, 179
Dispersion parameter, 165
Diagonalization technique, 80, 125, 154
Subject Index
Direction-finding, 125
Disutility functions, 297
early or late arrival, 209
for departure time choice, 210
for transit, 230
for auto, 230
scaling parameter, 231
Dynamic network models, 6
Dynamic process, 18
Dynamic route choice models, 103, 110, 112, 120, 141, 243, 267
Dynamic route guidance, 3
Dynamic traffic assignment, 103, 110, 112, 120, 141, 243, 267
Dynamic travel choice models, 12, 225
Dynamic User-Optimal (DUO), 103, 110, 112, 120, 141, 243, 267
instantaneous route choice, 103, 110, 112, 120, 243
ideal route choice, 141, 267
departure time/route choice, 210, 291
departure time/mode/route choice, 225
Dynamic system, 18
Dynamic System-Optimal (DSO), 313
objective functions, 313
total travel time minimization, 315
route choice with elastic departure times, 321
congestion pricing, 328
congestion level, 315
Enumerating routes, 144, 181, 252
Entropy functions, 169
379
Equality and inequality constraints, 28
Equivalence analysis, 108
Equivalent single level program, 214, 240
Estimated travel time, 90, 120, 167
Evacuation problems, 326
Example networks, 91, 100, 146, 253
Exit flow, 7, 9
variable, 9, 10
function, 7
FeaSible region, 60
Feedback control, 22
First-in-first-out (FIFO), 90
Flow conservation, 83
link, 84
node, 84
origin node, 85
destination node, 85
Flow-dependent, 181
Flow-independent, 181
Flow propagation, 87, i05, 223
type I, 88
type II, 89
Follower problem, 45
Forward pass, 184, 189
Frank-Wolfe algorithm, 77, 120
step size, 77
descent direction, 77
Freeway segment, 349
Games, 43
dynamic, 44 Nash,44
380
static, 43
Stackelberg, 43
Gradient, 59
Gumbel distribution, 176
Hamiltonian, 23
Hessian matrix, 60
Hierarchy of dynamic route choice models, 9
Hierarchy of dynamic travel choice models, 12
HOV, 354
Ideal DUO, 141
travel-tirne-based, 143 travel-cost-based, 273
Ideal SDUO, 173
Incident management, 357
Inflow, 83
Instantaneous DUO, 101
link-time-based, 103
link-cost-based, 260
route-time-based, 244
route-cost-based, 250
Instantaneous SDUO, 167
Instantaneous travel time, 86
instantaneous link travel time, 86 instantaneous route travel time,
86 minimal instantaneous route
travel time, 86
Intersection, 36
Isoperimetric O-D departure condition, 322
Iteration, 124
inner iteration, 124 outer iteration, 124
IVHS, 1,353
AHS, 361
APTS ATIS, 3
ATMS, 3
Subject Index
implementation issues, 353
data requirements, 362
Jacobian matrix, 286
Karush-Kuhn-Tucker conditions, 62
Lagrange multiplier, 23
Lagrangian, 61
Leader problem, 45
Likelihood of link usage, 185, 189
Line search, 124
Linear programming, 62
Linear regulator, 24
Link capacity, 93
maximal number of vehicles, 93
maximal exit flow rate, 94
Link travel time functions, 86, 337
cruise time, 338, 342
queuing delay, 339
Greenshields formula, 341 Akcelik's formula, 345
Local minimum, 60
Logit route choice, 166
Logit-type SDUO, 161, 181
Lower level problem, 208, 231, 357
'Mathematical programming, 59
unconstrained minimization, 59
nonlinear program, 60, 63, 64
bilevel, 65
Main problem variables, 121
Subject Index
Mean instantaneous travel times, 163
Mean actual travel times, 164
Method of successive averages (MSA),194
Minimal-cost route search, 124
flow propagation constraints in, 133
expanded time-space network, 126
feasible subroute, 133
cost adjustment, 133
Minimal travel time, 109, 144
instantaneous, 109
actual,144
Mode choice, 225
Multi-group models, 249, 259, 274, 281
instantaneous route choice, 249, 259
ideal route choice, 274, 281
Multi-group travelers, 227, 355
by income and age, 227
by route diversion willingness, 249
by driving behavior, 250
by travel choice criteria, 355
Network flow constraints, 83
Necessary conditions, 23
Network data, 363
geometry, 363 control, 363
conservation, 83 propagation, 87
FIFO, 90 capacity, 93
oversaturation, 94
Number of vehicles, 83
Objective function, 20
Operating cost, 232, 250
381
Optimal control problem, 17, 53, 103, 149, 165, 177
bilevel, 47
closed-loop, 22
continuous, 22
discrete, 54
fixed end, 23, 28, 40, 54
free end, 27, 30, 41
hierarchical, 42
open-loop, 22
O-D, 114, 136, 219
One-dimensional search, 75, 125
Optimality conditions, 111, 169, 213, 237
Optimization problem, 69
Oversaturation, 93
spill back constraints, 94
Parallel routes, 99
Parameters, 114
of link travel time function, 114
for departure time choice, 210 for mode choice, 230
Penalty, 116
Penalty for late arrival, 210
Penalty method, 152
Perceived actual travel times, 164
Perceived instantaneous travel times, 163
Performance measure, 20
Perfect information, 143
382
Pontryagin's Minimum (or Maximum) Principle, 24
Positive definite, 60
positive semidefinite, 60
strongly positive definite, 60
Queuing delay, 86, 325
instantaneous, 86, 103
Random error, 165
Random utility theory, 166
Recursive formula, 87, 183
Relaxation method, 80, 125, 154
double, 294
Riccati equation, 25
Round-off, 120
Route choice conditions, 109, 144
ideal DUO, 144 ideal SDUO, 175. instantaneous DUO, 109
instantaneous SDUO, 166
Route choice criteria, 355
Route travel times, 86, 87
mean instantaneous, 171 mean actual, 183
actual, 87
instantaneous, 86
Running time, 86, 103
Salvage cost, 21, 116
Saturation flow, 36
Signal controlled arterial, 340
Simultaneous travel choice, 229
Spill back constraints, 94, 322
State variable, 18, 83
State equation, 19, 84
Subject Index
Stochastic models, 161, 181
dispersion parameter, 165
dispersed route choice, 179
efficient route, 182
instantaneous SDUO, 161
ideal SDUO, 181 Gumbel distribution, 176 randomness assumptions, 162 perceived instantaneous travel
times, 163 mean instantaneous travel times,
163 perceived actual travel times, 164
mean actual travel times, 164
flow-independent instantaneous SDUO, 183
flow-independent ideal SDUO, 188
logit route choice, 166
logit route flow constraint, 176 variance, 166 entropy functions of route flows,
169
Stratification of travelers, 227, 249, 355
Subproblem variables, 121
Super destination, 129
Test networks, 114, 136, 200, 218
Time interval, 54
Time-optimal problems, 33, 326
Time period, 83, 116
Time-space network, 126
solving LP problems, 126 expansion, 131 dummy node, 132 one-to-one, 131 many-to-many, 133
Toll, 360
Subject Index
bottleneck, 360 link and route, 360
area congestion, 360
Traffic control, 356
bilevel program, 357
Traffic How data, 364
Traffic prediction, 353
Transit, 3
APTS, 3 transit information center, 3
Transportation planning, 5, 361
Transversality conditions, 23
Traveler information, 365
Travel time, 86, 338
actual (future) link travel time, 86, 339
actual route travel time, 87, 339 dynamic travel ti"me, 86, 338
estimated link travel time, 90 instantaneous link travel time,
86, 338 instantaneous route travel time,
86 minimal actual route travel time,
87, 143 minimal instantaneous route
travel time, 86
Travel time function, 86, 338
for various purposes, 338 for longer horizon, 340 for short horizon, 346 for arterial, 340, 346 for freeway segment, 349
Total travel time, 325
Two-point boundary conditions, 23
Two-stage programs, 234
first stage, 230 second stage, 231
Unit route travel cost, 118
383
Upper level problems, 211, 233, 357
Used links, 101
Used routes, 101
User-equilibrium, 4
User-optimal, 4
Variance, 166
Variational inequality, 68, 243, 267, 291, 331, 335
definition, 68
existence, 72
uniqueness, 74
necessity, 246, 257, 270, 279, 295 sufficiency, 247, 257, 271, 279,
296
ideal route choice, 267
instantaneous route choice, 243 departure time/route choice, 291 link-cost-based, 261, 282, 301 link-time-based, 257, 278 multi-group, 252, 261, 275, 282 route-cost-based, 246, 275, 295 route-time-based, 246, 270, relaxation, 261, 283
Wardrop's UE, 4
Author Index
Abdulaal M., 226
Abkowitz M., 8, 205
Akcelik R., 344, 345
Alfa A.S., 194, 201
Barcelo J., 8
Bard J.F., 82
Bazaraa M.S., 82
Beckmann M., 4, 328
Ben-Akiva M., 3, 8, 205
Bernstein D., 205, 254, 266, 311
Boyce D.E., 2, 4, 5, 8, 9, 226, 266, 311, 312
Bryson Jr., A.E., 52, 81
Burrow LA., 345
Canon M.D., 82
Carey M., 7, 97, 117, 118,335
Cascetta E., 7, 161
Cesari L., 82
Chang G.L., 7, 8, 336
Chatterjee A., 5
Chen M., 194, 201
Codina E., 8
Codelli D.K., 249
Cruz J.B. Jr., 43, 47, 52, 228
Cullum, Jr., C.D., 82
Cyna M., 205
Dafermos S.C., 4, 226, 266, 328
Daganzo C.F., 5, 97, 161, 201 311 351 ' ,
de Palma A., 8, 205, 328
Dial R.B., 5, 11, 164, 184, 201, 253
Fambro, D.B., 344
Fisk C., 161, 201
Florian M., 4, 5, 226
Frank M., 120, .216
Friesz :r.L., 2, 5, 7, 8, 117,205,254 266, 311 '
Ghali M., 6, 206, 311, 328
Greenshields B., 341
Hendrickson C., 8, 205 .
Herman R., 205
Ho J .K., 8, 335
Ho P.K., 7, 336
Ho Y.C., 52, 81
Hollis E.M., 344
Hu T., 6
Hurdle V.F., 6
Inaudi D., 7
Inouye H., 152
Janson B.N., 7, 8, 205,311
386
J ayakrishnan R., 6
Kamien M.L., 52
Kaufman D.E., 6
Kaysi 1.,3
Kimber R.M., 344
Kinderlehrer D., 82
Kirk D.E., 52
Koutsopoulos H., 3
Kuhn H., 81
Kuo B.C., 82
Lafortune S., 6
LeBlanc L.J., 4, 8, 9, 120, 226, 311, 312
Lefevre C., 8, 205
Leventhal T., 135
Lieberman E.B., 94, -97
Lindsey R., 328
Litinas N., 8, 205
Lo H.K., 5
Luenberger D.G., 82
Luque F.J., 2, 7,117
Mahmassani H.S., 6, 8, 126, 205, 336
Marquis G., 7
McGuire C.B., 4, 328
McShane W.R., 342
Merchant D.K., 6, 7,117, 118,335
Messer C.J., 344
Morlok E.K., 4, 120
Mouskos K., 126
Nagurney A., 4, 73, 82, 266, 312
Author Index
Nemhauser G.L., 6, 7, 117, 118, 135, 335
Newell G.F., 311, 349, 351
Nguyen S., 4, 226
Niedringhaus W.P., 249
Plank E., 8, 205
Pierskalla W.P., 4, 120
Polak E., 82
Pontryagin L.S., 24
Powell W.B., 194, 201
Ran B., 7, 8, 9, 311, 312, 335
Rathi A.K., 5, 365
Richards S., 5
Roess R.P., 342
Rouphail N.M., 344, 345
Russak B.L, 52
Sage A.P., 52, 81
Santiago A.J., 365
Schwartz N.L., 52
Sengupta R., 6
Sheffi Y., 4, 5, 82, 90, 161, 165, 166, 194201
Sherali H.D., 82
Shetty C.M., 82
Shimazaki T., 7
Singh M.G., 52
Small K.A., 328
Smith M.J., 4, 6, 206, 254, 266, 311, 328
Smith R.L., 6
Smith T.E., 5, 8, 205, 254, 266, 311
Solanki R.S., 365
Author Index
Sparrow F.T., 4
Stampacchia G., 82
Stackelberg von H., 43
Tabak D., 82
Takaba S., 346
Teply S., 344
Titli A., 52
Tobin R.L., 2, 5, 7, 8, 117, 205, 254, 266,311
Trotter, Jr. L., 135
Tucker A.W., 81
Van Aerde M., 6
Vythoulkas P.C., 7, 162
Wang P.T.R., 249
Wardrop J.G., 4
Webster F.V., 344
Wegmann F., 5
Wei C.H., 7, 336
White, III. C.C., 52, 81
Wie B.-W., 2, 5,7,8,117,205,254, 266,311
Wilson A.G., 226
Winsten C.B., 4, 328
Wolfe P., 120, 216
Yagar S., 6, 365
Young B.S., 249
387
List of Figures
1.1 Structure of an Integrated APTSj ATMSj ATIS System. 1.2 A Hierarchy of Dynamic Route Choice Models 1.3 A Hierarchy of Dynamic Travel Choice Models 1.4 Logical Flowchart of the Chapters ...... .
2.1 Closed-Loop and Open-Loop Optimal Controls 2.2 Four-Leg Intersection .............. . 2.3 Cumulative Arrivals and Departures at the Intersection
3 9
12 14
22 36 39
4.1 Flow Variables for Link a .. . . . . . . . . . . . . 84 4.2 Flow Conservation at Node j . . . . . . . . . . . . 85 4.3 Cumulative Entering and Exiting Flows on Link a 88 4.4 Flow Propagation on Link a . 89 4.5 Example Network. . . . . . 91 4.6 Example of Spillback . . . . 95 4.7 Queuing Delay at Origin r . 97
5.1 Example Network. . . . . . 100 5.2 Dynamic User-Optimal Inflows and Travel Times 102 5.3 Example Network with Inflow. 106 5.4 Test Network . . . . . . . . . . . . . 114
6.1 Flowchart of the Solution Algorithm 126 6.2 Expansion for Link a for 3 Time Periods. 127 6.3 Expansion for Link a for 3 Time Periods (m is a destination) 128 6.4 Expansion for 3-Link Network for 3 Time Periods. 129 6.5 Expansion of Example Network (2 links) . . 130 6.6 Test Network . . . . . . . . . . . . . . . . . 136
7.1 Relationship of pr6(t) and Er6 (t) to 1I'r6(t) 7.2 Two-Link Network ......... . 7.3 Flowchart of the Solution Algorithm
8.1 Relation of F;6(t) and E;6(t) to 7J;6(t) 8.2 Toward Realistic SDUO Route Choice Models.
145 146 158
175 180
390 LIST OF FIGURES
9.1 Flowchart of the Instantaneous Solution Algorithm. 196 9.2 Flowchart of the Ideal Solution Algorithm 199 9.3 Test Network. . . . . . . . . . . . . . 200
10.1 Bilevel Choice Program Formulation 208 10.2 Bonus/Penalty for Early/Late Arrival 210 10.3 Flowchart of the Solution Algorithm 217 lOA Test Network . . . . . . . . . . 218 10.5 Flow Propagation on Link 2-4 ... 223
11.1 Two-Stage Simultaneous Travel Choice Model . 229 11.2 Arrival Time Disutility. . . . . . . . . . . . . . 232 11.3 Decision Variables in the Two-Stage Travel Choice Program. 238
12.1 Example Grid Network. . . . . . . . 253
13.1 Example Network with Two Origins 287 13.2 Flowchart of the Double Relaxation Procedure 290
14.1 Arrival Time Disutility. . . . . . . . . . 293
15.1 Isoperimetric O-D Departure Condition 322 15.2 Optimal Assignment Time in DSO Route Choice Problem 325 15.3 Optimal Time Period in Time-Optimal Problem 328
16.1 Traffic on an Arterial Road Link. . . . . . . . . . 341
17.1 A Bilevel Program for Dynamic Traffic Prediction and Control 357 17.2 A Segregated Automated Highway System. . . . . . . . . . .. 361
List of Tables
5.1 Parameters of Link Travel Time Functions. . . . . . . . . . .. 114 5.2 Required Flows from Origin 1 to Destination 4 . . . . . . . .. 114 5.3 Optimal Numbers of Vehicles, Inflows, Exit Flows and Travel
Times . . . . . . . . . . . . . . . . . . . . . 115 5.4 Dynamic User-Optimal Route Travel Times 115
6.1 Parameters of Link Cost Functions . . . . . 136 6.2 O-D Trip Table for Each Time Interval k 136 6.3 Optimal Trajectories of Link Flows and Travel Times 137 6.4 Comparison of Instantaneous Route Travel Times. 139
9.1 Required Flows from Origin 1 to Destination 4. . . 200 9.2 Parameters of Link Travel Time Functions for Instantaneous
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 201 9.3 Parameters of Link Travel Time Functions for Ideal Model. .. 201 9.4 Optimal Link Flows and Travel Times for Instantaneous Model 202 9.5 Instantaneous Route Travel Times . . . . . . . . . . . 202 9.6 Optimal Link Flows and Travel Times for Ideal Model 203 9.7 Ideal Route Travel Times . . . . . . . . . . 203
10.1 Parameters of Link Travel Time Functions. 218 10.2 Departure Flow Patterns from Origin 1 to Destination 4 219 10.3 Optimal Link Flows and Travel Times for Initial O-D Flows. 221 10.4 Optimal Link Flows and Travel Times for Improved O-D Flows 222
11.1 Stratification of Travelers Based on Income and Age 227
12.1 Stratification of Travelers Based on Income and Age 249 12.2 Stratification of Travelers Based on Route Diversion Willingness 249 12.3 Stratification of Travelers Based on Driving Behavior . 250 12.4 Number of Nodes, Links and Routes . . . . . 253
17.1 Route Choice Criteria for Different Travelers 17.2 Groups of Travelers and Travel Choice Criteria
355 355
