Queue Length Estimation Based on Probe Vehicle Data at Signalized Intersections

<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" rowspan="2">Error indexes</td><td class="align_center" colspan="3">Probe vehicle penetration</td></tr><tr class="thead"><td class="align_center">50 (%)</td><td class="align_center">25 (%)</td><td class="align_center">10 (%)</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left"><span style="width: 28.5285ptpx;"><svg height="11.8174pt" id="M104" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 28.5285 11.8174" width="28.5285pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M871 0V33C783 41 780 45 777 152L768 506C765 610 771 609 860 617V650H683L453 157L228 650H59V617C150 609 154 606 146 481L132 275C124 170 117 125 112 93C105 50 84 39 27 34V0H267V34C200 39 176 48 173 93C170 130 171 172 176 256L190 540H192L414 8H438L682 554H685L689 152C689 45 686 41 604 33V0H871Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.151,3.132)"><path d="M682 0V33C615 38 603 49 571 134C507 305 441 494 378 665L343 655L136 136C101 48 86 41 22 33V0H246V33C170 41 161 50 183 112C196 152 209 192 224 232H441C461 176 478 126 493 87C504 49 499 41 433 33V0H682ZM425 279H242C273 363 303 448 335 533H337L425 279Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.548,3.132)"><path d="M522 166C507 123 488 90 472 71C449 44 419 38 347 38C296 38 261 38 242 51C223 63 217 85 217 132V315H311C398 315 406 310 419 239H453V433H419C406 365 401 358 311 358H217V580C217 609 219 612 251 612H331C400 612 427 604 440 584C453 561 463 541 472 498L506 502C501 558 497 627 497 650H43V618C122 610 130 609 130 520V128C130 46 121 40 30 32V0H521C529 30 552 128 557 162L522 166Z"></path></g></svg></span></td><td class="align_center">5.56</td><td class="align_center">13.32</td><td class="align_center">18.97</td></tr><tr><td class="align_left"><svg height="11.8631pt" id="M105" style="vertical-align:-3.227201pt" version="1.1" viewbox="-0.0498162 -8.6359 34.3652 11.8631" width="34.3652pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M871 0V33C783 41 780 45 777 152L768 506C765 610 771 609 860 617V650H683L453 157L228 650H59V617C150 609 154 606 146 481L132 275C124 170 117 125 112 93C105 50 84 39 27 34V0H267V34C200 39 176 48 173 93C170 130 171 172 176 256L190 540H192L414 8H438L682 554H685L689 152C689 45 686 41 604 33V0H871Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.151,3.132)"><path d="M682 0V33C615 38 603 49 571 134C507 305 441 494 378 665L343 655L136 136C101 48 86 41 22 33V0H246V33C170 41 161 50 183 112C196 152 209 192 224 232H441C461 176 478 126 493 87C504 49 499 41 433 33V0H682ZM425 279H242C273 363 303 448 335 533H337L425 279Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.548,3.132)"><path d="M639 21C616 28 593 39 566 68C542 92 523 117 486 170C457 215 415 282 397 314C472 346 524 398 524 485C524 545 497 590 456 617C417 641 369 650 296 650H43V617C122 612 130 608 130 523V129C130 45 122 38 38 33V0H306V33C225 38 216 45 216 129V282H249C302 282 319 270 336 243C365 195 401 132 436 84C483 18 525 -5 597 -8C610 -9 622 -9 635 -9L639 21ZM216 319V559C216 586 219 596 227 603S250 613 281 613C356 613 429 576 429 469C429 416 413 379 374 348C349 327 316 319 265 319H216Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,28.364,3.132)"><path d="M522 166C507 123 488 90 472 71C449 44 419 38 347 38C296 38 261 38 242 51C223 63 217 85 217 132V315H311C398 315 406 310 419 239H453V433H419C406 365 401 358 311 358H217V580C217 609 219 612 251 612H331C400 612 427 604 440 584C453 561 463 541 472 498L506 502C501 558 497 627 497 650H43V618C122 610 130 609 130 520V128C130 46 121 40 30 32V0H521C529 30 552 128 557 162L522 166Z"></path></g></svg> (%)</td><td class="align_center">11.27</td><td class="align_center">27.77</td><td class="align_center">39.12</td></tr><tr><td class="align_left"><span style="width: 32.4079ptpx;"><svg height="11.9316pt" id="M106" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 32.4079 11.9316" width="32.4079pt" 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="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M639 21C616 28 593 39 566 68C542 92 523 117 486 170C457 215 415 282 397 314C472 346 524 398 524 485C524 545 497 590 456 617C417 641 369 650 296 650H43V617C122 612 130 608 130 523V129C130 45 122 38 38 33V0H306V33C225 38 216 45 216 129V282H249C302 282 319 270 336 243C365 195 401 132 436 84C483 18 525 -5 597 -8C610 -9 622 -9 635 -9L639 21ZM216 319V559C216 586 219 596 227 603S250 613 281 613C356 613 429 576 429 469C429 416 413 379 374 348C349 327 316 319 265 319H216Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.901,3.132)"><path d="M871 0V33C783 41 780 45 777 152L768 506C765 610 771 609 860 617V650H683L453 157L228 650H59V617C150 609 154 606 146 481L132 275C124 170 117 125 112 93C105 50 84 39 27 34V0H267V34C200 39 176 48 173 93C170 130 171 172 176 256L190 540H192L414 8H438L682 554H685L689 152C689 45 686 41 604 33V0H871Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.109,3.132)"><path d="M416 501L399 642C356 655 314 665 271 665C140 665 63 582 63 486C63 372 163 325 229 290C304 250 359 217 359 142C359 70 316 25 240 25C138 25 94 125 78 186L44 178C52 123 64 45 72 21C81 16 96 8 121 0S179 -15 220 -15C353 -15 445 68 445 176C445 289 350 335 270 375C191 414 143 449 143 520C143 572 177 627 253 627C340 627 366 556 382 495L416 501Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,26.413,3.132)"><path d="M522 166C507 123 488 90 472 71C449 44 419 38 347 38C296 38 261 38 242 51C223 63 217 85 217 132V315H311C398 315 406 310 419 239H453V433H419C406 365 401 358 311 358H217V580C217 609 219 612 251 612H331C400 612 427 604 440 584C453 561 463 541 472 498L506 502C501 558 497 627 497 650H43V618C122 610 130 609 130 520V128C130 46 121 40 30 32V0H521C529 30 552 128 557 162L522 166Z"></path></g></svg></span></td><td class="align_center">6.94</td><td class="align_center">15.94</td><td class="align_center">22.53</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Error indexes under different probe vehicle penetration.</div>

Journal of Advanced Transportation

tab3

Table 3

Table 3: Queue Length Estimation Based on Probe Vehicle Data at Signalized Intersections 