A Stochastic User Equilibrium Formulation for the Cumulative Prospect Theory-Based Cross-Nested Logit

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Number of iterations</td><td class="align_center" colspan="3">Convergence criterion <svg height="15.7007pt" id="M137" style="vertical-align:-3.2402pt" version="1.1" viewbox="-0.0498162 -12.4605 60.0248 15.7007" width="60.0248pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.331,-5.741)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.11,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.373,0)"><path d="M52 442L22 406L27 394H92V108C92 45 88 39 30 32V0H302V32C227 39 220 45 220 108V394H321C335 401 339 431 335 442H220L218 477C214 562 214 597 220 616C224 631 233 642 251 642C279 642 311 617 335 593C345 583 355 583 369 593C384 605 395 618 399 629C406 644 405 659 391 673C374 689 349 701 309 703C261 697 226 679 190 649C133 601 112 553 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481 -153 481 -39C481 66 390 84 327 84C295 84 267 82 235 82C187 81 170 103 170 120C170 131 177 140 184 148C199 146 216 143 234 143C332 143 424 195 424 299C424 333 413 356 398 376L455 371C474 382 492 414 498 432L494 439ZM235 417C284 417 305 359 305 294C305 220 284 180 245 180C198 180 176 236 176 306C176 379 205 417 235 417ZM242 -21C280 -21 302 -23 329 -29C361 -38 385 -59 385 -95C385 -148 340 -189 264 -189C185 -189 135 -141 135 -92C135 -72 144 -57 158 -42C172 -26 194 -21 242 -21Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,54.702,-5.741)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"></path></g></svg></td></tr><tr class="thead"><td class="align_left"><span style="width: 6.6501ptpx;"><svg height="6.1673pt" id="M138" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.6501 6.1673" width="6.6501pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"></path></g></svg></span></td><td class="align_center">MSA</td><td class="align_center">MSWA</td><td class="align_center">SRA</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">100</td><td class="align_center">75.94</td><td class="align_center">491.00</td><td class="align_center">257.91</td></tr><tr><td class="align_left">200</td><td class="align_center">24.31</td><td class="align_center">348.15</td><td class="align_center">22.24</td></tr><tr><td class="align_left">400</td><td class="align_center">12.13</td><td class="align_center">19.18</td><td class="align_center">4.62</td></tr><tr><td class="align_left">800</td><td class="align_center">6.06</td><td class="align_center">2.39</td><td class="align_center">0.36</td></tr><tr><td class="align_left">1600</td><td class="align_center">3.03</td><td class="align_center">0.30</td><td class="align_center">0.01</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Computational efficiency of MSA, MSWA, and SRA.</div>

Discrete Dynamics in Nature and Society

tab3

Table 3

Table 3: A Stochastic User Equilibrium Formulation for the Cumulative Prospect Theory-Based Cross-Nested Logit 