Mathematics in Transport: Selected Proceedings of the 4th IMA International Conference on Mathematics in Transport In honour of Richard Allsop

Front Cover......Page 1
Mathematics in Transport......Page 4
Copyright Page......Page 5
Table of Contents......Page 6
Preface......Page 10
Tribute to Richard Allsop......Page 12
Contributors......Page 14
ABSTRACT......Page 18
ROAD JUNCTION DESIGN IN TRAFFIC MANAGEMENT......Page 19
ELEMENTS OF A ROAD JUNCTION AND ITS VEHICULAR TRAFFIC......Page 20
SIGNAL-CONTROLLED JUNCTIONS......Page 21
ROUNDABOUTS AND PRIORITY JUNCTIONS......Page 22
References......Page 28
ABSTRACT......Page 30
COLLISIONS......Page 31
FRONTAL CRASH COMPATIBILITY......Page 32
SIDE IMPACTS......Page 36
ARE SUVS A PROBLEM?......Page 37
IS ANYTHING BEING DONE?......Page 39
CHANGES IN EXPOSURE PATTERNS......Page 40
THE ENVIRONMENT......Page 41
RIDER......Page 42
References......Page 43
ABSTRACT......Page 44
THE BASIC EQUILIBRIUM MODEL, MODEL 0......Page 45
EQUILIBRIUM MODEL 1: A RIGID DEMAND MODEL......Page 46
EQUILIBRIUM MODEL 2: A VARIABLE DEMAND MODEL USING MODEL 1 WITH AN EXTRA ROUTE......Page 49
EQUILIBRIUM MODEL 3: MODEL 2 PLUS LOGIT ROUTE-CHOICE......Page 51
MODEL 4: A DIFFERENT FORM OF EQUILIBRIUM MODEL 3 ABOVE......Page 53
EXPLORATORY COMPUTATIONAL TESTS......Page 54
CONCLUSION......Page 58
References......Page 59
ABSTRACT......Page 62
INTRODUCTION......Page 63
SYSTEM OPTIMISATION UNDER DETERMINISTIC ASSIGNMENT WITH ELASTIC DEMAND......Page 64
ACHIEVING SYSTEM OPTIMISING FLOW PATTERNS BY TOLLING UNDER STOCHASTIC ASSIGNMENT WITH ELASTIC DEMAND......Page 67
COMPARISON OF TOLLING TO ACHIEVE SYSTEM OPTIMAL FLOW PATTERNS WITH ELASTIC DEMAND TO MARGINAL SOCIAL COST PRICE TOLLING UNDER SUEED......Page 70
SUMMARY......Page 72
References......Page 73
ABSTRACT......Page 76
INTRODUCTION......Page 77
PROBLEM FORMULATION......Page 78
A NOVEL SOLUTION FOR TOP......Page 80
NUMERICAL CALCULATIONS......Page 81
CONCLUSIONS AND FUTURE WORK......Page 82
References......Page 83
ABSTRACT......Page 88
INTRODUCTION......Page 89
A CENTRAL VARIABLE DEMAND EQUILIBRIUM MODEL......Page 92
THE COBWEB AND FIVE OTHER ALGORITHMS......Page 97
ALGORITHM 1: A DEVELOPMENT OF THE COBWEB......Page 98
ALGORITHM 2: A SINGLE DIRECTION ALGORITHM......Page 100
ALGORITHM 3: THE \"MOST OBVIOUS\" ALGORITHM......Page 101
ALGORITHM 4: THE MAIN TWO-DIRECTION ALGORITHM......Page 102
TEST RESULTS USING SIMPLE EXAMPLE NETWORKS......Page 104
CONCLUSION......Page 107
References......Page 108
THE TWO-DIRECTION METHOD WITH MANY ROUTES......Page 109
ABSTRACT......Page 114
A SIMPLE MODEL......Page 115
RING MODEL WITH TIME DELAY INCLUDED......Page 117
STABILITY OF THE RING MODEL......Page 121
References......Page 126
ABSTRACT......Page 128
BACKGROUND......Page 129
THE RING NETWORK AND CALIBRATION DATA SOURCES......Page 130
A CALIBRATION AND VALIDATION FRAMEWORK......Page 131
SUMMARY......Page 138
References......Page 139
ABSTRACT......Page 142
CAR-FOLLOWING MODELS......Page 143
COLLECTING CAR-FOLLOWING DATA......Page 147
ANALYSING THE DATA......Page 150
RESULTS......Page 151
CONCLUSIONS......Page 153
References......Page 154
ABSTRACT......Page 156
CYCLING, POLICY AND USAGE DATA IN THE UK......Page 157
DEVELOPMENT OF MONITORING TECHNIQUES FOR THE NATIONAL CYCLE NETWORK......Page 160
COMPARISON OF THE DATA SOURCES......Page 165
DISCUSSION OF THE DEVELOPMENTS REQUIRED......Page 166
References......Page 167
ABSTRACT......Page 170
INTRODUCTION......Page 171
MCP SCHEMES IN AN INTEGRATED LOCATION/ TRANSPORT MODEL......Page 172
SENSITIVITY ANALYSIS AND OPTIMAL PRICING SCHEME DESIGN......Page 175
A NUMERICAL EXAMPLE......Page 177
References......Page 181
ABSTRACT......Page 184
CONVENTIONAL APPROACH TO MODELLING OF ROAD ACCIDENTS......Page 185
METHOD USED IN DISEASE MAPPING......Page 187
BAYESIAN MODELLING OF ROAD ACCIDENTS WITH SPATIAL EFFECTS......Page 188
CONCLUSION......Page 195
References......Page 196
ABSTRACT......Page 198
INTRODUCTION......Page 199
THE D-SA CONTROL STRATEGY......Page 200
THE DILEMMA ZONE ANALYSIS......Page 203
NUMERICAL CALCULATIONS......Page 205
SUMMARY AND CONCLUSIONS......Page 207
References......Page 209
ABSTRACT......Page 212
INTRODUCTION: RANDOM UTILITY MAXIMISATION......Page 213
‘INVARIANT’ RUM......Page 215
GEV MODELS......Page 219
Acknowledgements......Page 225
References......Page 226
ABSTRACT......Page 228
INTRODUCTION......Page 229
STOCHASIC DEMAND......Page 230
FORMULATION......Page 232
EXAMPLE......Page 233
References......Page 235
ABSTRACT......Page 236
THE DYNAMIC TRAFFIC MODEL......Page 237
EXISTENCE OF EQUILIBRIUM......Page 239
CONVEXITY OF THE SET OF EQUILIBRIA......Page 243
Acknowledgements......Page 245
References......Page 246
ABSTRACT......Page 248
DEFINITION OF SYSTEM......Page 249
CONDITION OF DELAY AT BOTTLENECKS......Page 252
PROOF OF EQUIVALENCE BETWEEN EQUILIBRIUM AND OPTIMIZATION......Page 253
ANALYSIS ON MARGINAL COST......Page 259
DISCUSSIONS......Page 260
References......Page 261
ABSTRACT......Page 262
NETWORK LOADING MODELS AND COST FUNCTIONS......Page 263
DYNAMIC EQUILIBRIUM CONDITION......Page 266
SYSTEM OPTIMAL ASSIGNMENT AND EXTERNALITY......Page 267
EXAMPLE CALCULATIONS......Page 268
Acknowledgements......Page 273
References......Page 274
ABSTRACT......Page 276
QUEUING PROCESSES IN ROAD TRAFFIC......Page 277
THE M/M/1 QUEUE......Page 278
THE M/D/1 QUEUE......Page 279
GENERAL QUEUES AND THE SHEARING TRANSFORMATION......Page 280
CALCULATION AND SIMULATION......Page 281
NON-EQUILIBRIATION OF QUEUE STATES DURING PEAKS......Page 284
SOURCES OF INACCURACY IN THE SHEARED QUEUE......Page 286
ACCURACY OF INITIAL QUEUE MODEL BEHAVIOUR......Page 289
AN ALTERNATIVE MODEL OF QUEUE DEVELOPMENT......Page 291
TESTS OF AN INTEGRATED COMPUTER MODEL......Page 293
CONCLUSION......Page 294
References......Page 295
ABSTRACT......Page 296
BACKGROUND......Page 297
THE MBA AND FBA MODELS......Page 298
NUMERICAL RESOLUTION OF THE FBA MODEL......Page 301
A NEW NUMERICAL SCHEME BASED ON THE MBA MODEL......Page 303
References......Page 308
ABSTRACT......Page 310
THE ARZ MODEL......Page 311
RESOLUTION OF ARZ MODEL......Page 314
NUMERICAL EXAMPLE......Page 319
Acknowledgements......Page 322
References......Page 323
ABSTRACT......Page 324
INTRODUCTION......Page 325
CONSTRAINT SETS FOR SIGNAL SETTINGS......Page 326
THE SIGNALISED CELL TRANSMISSION MODEL......Page 328
NUMERICAL EXAMPLES......Page 331
References......Page 334
ABSTRACT......Page 338
FORMULATION......Page 339
SOLUTION ALGORITHM FOR α*......Page 343
A NUMERICAL EXAMPLE......Page 345
DISCUSSION......Page 347
References......Page 348
ABSTRACT......Page 350
THE LAMBERT W-FUNCTION......Page 351
THE CAR-FOLLOWING MODEL......Page 354
ROUTE CHOICE......Page 356
CRASHES AND THE POISSON-LOGNORMAL......Page 357
CONCLUSION......Page 361
References......Page 362
APPENDIX: R CODE FOR LAMBERT W-FUNCTION......Page 364
ABSTRACT......Page 366
THE LWR MODEL AND ITS RESOLUTION......Page 367
INTRODUCING BOUNDARY CONDITIONS......Page 370
PRACTICAL RESOLUTION OF AN EXTENDED RIEMANN PROBLEM......Page 372
APPLICATION TO THE WAVE TRACKING RESOLUTION SCHEME......Page 373
ILLUSTRATION OF THE METHOD......Page 376
CONCLUSION AND PERSPECTIVES......Page 378
References......Page 379
ABSTRACT......Page 380
INTRODUCTION......Page 381
CONTINUUM MODELS: WHY AND WHEN?......Page 382
KINEMATIC WAVE MODELS......Page 383
HIGHER ORDER MODELS......Page 386
TOMORROW......Page 387
References......Page 388
ABSTRACT......Page 390
INTRODUCTION......Page 391
DESCRIPTION OF THE GENERAL METHOD......Page 392
FURTHER REMARKS......Page 399
ANALYTICAL EXAMPLES......Page 403
CONCLUDING REMARKS......Page 410
References......Page 411
ABSTRACT......Page 414
INTRODUCTION......Page 415
DEFINITIONS AND NOTATION......Page 416
DUE AND SUE SENSITIVITY ANALYSIS: THEORETICAL ISSUES......Page 417
DUE SENSITIVITY ANALYSIS: PRACTICAL ISSUES......Page 418
SUE SENSITIVITY ANALYSIS: PRACTICAL ISSUES......Page 419
References......Page 427