Empirical Invistigation of Day-To-Day Variability In Driver Travel Behaviour The See you next Wednesday Effect Department of Mathematics, University of York, YO10 5DD Universities Transport Studies Group, Bristol, January 2005
Outline 1 Day-to-Day Driver Variability Recurrence Rate Definition Previous Research 2 Data Collection Methodology Lendal Bridge Study Fishergate Study 3 Raw Matching Recurrence Rates Model Fitting 4
Day-to-Day Driver Variability Day-to-Day Driver Variability Recurrence Rate Definition Previous Research The topic is that of ambient variability in road traffic how does traffic change between days when the network remains constant? Is the traffic on one day the same as the traffic the next day? Is a rush-hour composed of the same vehicles travelling day after day?
Day-to-Day Driver Variability Day-to-Day Driver Variability Recurrence Rate Definition Previous Research The topic is that of ambient variability in road traffic how does traffic change between days when the network remains constant? Is the traffic on one day the same as the traffic the next day? Is a rush-hour composed of the same vehicles travelling day after day? Obviously not or I wouldn t be asking these questions But how does the composition change as day follows day What factors affect the variability of rush hour
Recurrence Rate Definition Day-to-Day Driver Variability Recurrence Rate Definition Previous Research Given two time periods T 1 = (S 1, E 1 ) and T 2 = (S 2, E 2 ), the recurrence rate R(T 1, T 2 ) is given by Recurrence Rate R(T 1, T 2 ) = # vehicles seen in T 1 and T 2 # vehicles seen in T 1 Note that usually T 1 and T 2 are disjoint (for example, the rush hour on different days) Note also that R(T 1, T 2 ) R(T 1, T 2) if T 2 T 2 That is, the recurrence rate will usually be increased if the second time period examined is made larger
Previous Research Outline Day-to-Day Driver Variability Recurrence Rate Definition Previous Research The percentage of individuals in each sample who exhibit the same characteristic across all daysis extremely small [often] zero (Pendyala 2003) we are led to reject the view that travel is highly routinized in the restricted sense that every weekday is assumed to look much like every other weekday (Huff and Hanson 1986) A study of recurrence rates between two days in Leeds is given by (Bonsall et al 1984) The recurrence rate is less than 60% but depends strongly on the exact measure used Reviews are given by (Batley and Clegg 2001) and (Clegg 2004)
Data Collection Methodology Data Collection Methodology Lendal Bridge Study Fishergate Study Two studies took place in the city of York: Lendal Bridge and Fishergate Partial licence plate data was collected at several sites for several weeks The studies were centred around investigating interventions on the network Licence plate data was collected manually (in almost all cases by audio tape) All the data here is publicly available to researchers
Lendal Map Outline Data Collection Methodology Lendal Bridge Study Fishergate Study L K Lendal Bridge Pedestrian Area H G F I Station J Ouse Bridge E A Inner Ring Road Clifford s Tower and Castle Museum C N B Skeldergate Bridge River Ouse D M
Fishergate Map Outline Data Collection Methodology Lendal Bridge Study Fishergate Study Pedestrian Area Station H I J C Clifford s Tower and Castle Museum G Inner Ring Road D A B K F Detail of Scheme University A B C River Ouse E Outer Ring Road
Fishergate Description Data Collection Methodology Lendal Bridge Study Fishergate Study Day Survey Comment 25th June 2001 Before survey 26th June 2001 Before survey 27th June 2001 Before survey 28th June 2001 Before survey 29th June 2001 Before survey 2nd July 2001 Before survey Partial closure occurred at 9:15 and should not affect the data collected 3rd July 2001 During survey First day of partial closure 4th July 2001 During survey 5th July 2001 During survey 6th July 2001 During survey 11th July 2001 During survey 12th July 2001 During survey 13th July 2001 After survey Road works removed to ease traffic for a race meeting in York This can be considered to be an after survey day 16th July 2001 During Survey Road works put back in place
Raw Matching Recurrence Rates Model Fitting Empty match Lendal Sites L and M 28/6/00 540 530 520 Minutes past midnight 510 500 490 480 480 490 500 510 520 530 540 Minutes past midnight
Raw Matching Recurrence Rates Model Fitting Between days match Lendal Site M 6/9/00 7/9/00 540 530 520 Minutes past midnight 510 500 490 480 480 490 500 510 520 530 540 Minutes past midnight
Raw Matching Recurrence Rates Model Fitting Single day match Lendal Sites I and J 28/6/00 540 530 520 Minutes past midnight 510 500 490 480 480 490 500 510 520 530 540 Minutes past midnight
Raw Matching Recurrence Rates Model Fitting Lendal Site L 8:00 9:00 recurrence rate 27/6/00 28/6/00 6/9/00 7/9/00 8/9/00 27/6/00 1076 (997) 473 (390) 243 (178) 246 (181) 252 (188) 28/6/00 445 (367) 1098 (1015) 253 (187) 251 (186) 220 (156) 6/9/00 291 (213) 322 (239) 1051 (986) 454 (389) 399 (336) 7/9/00 296 (218) 321 (237) 456 (390) 1079 (1014) 432 (369) 8/9/00 310 (232) 288 (205) 411 (345) 443 (378) 1055 (992) 11/9/00 297 (219) 297 (214) 374 (308) 379 (314) 372 (309) 13/9/00 268 (190) 306 (223) 340 (275) 336 (271) 343 (279) 27/9/00 314 (236) 327 (244) 348 (282) 325 (260) 324 (260) 18/10/00 259 (181) 307 (223) 291 (226) 309 (244) 294 (230) 11/9/00 13/9/00 27/9/00 18/10/00 27/6/00 255 (188) 202 (143) 268 (201) 222 (155) 28/6/00 239 (172) 217 (158) 262 (196) 247 (180) 6/9/00 383 (316) 307 (248) 355 (288) 299 (232) 7/9/00 391 (324) 305 (246) 333 (266) 318 (251) 8/9/00 393 (326) 319 (260) 340 (273) 310 (243) 11/9/00 1084 (1016) 360 (301) 375 (308) 303 (236) 13/9/00 409 (342) 1100 (1041) 346 (279) 328 (261) 27/9/00 376 (309) 306 (247) 1067 (1000) 392 (325) 18/10/00 303 (236) 289 (230) 390 (323) 1041 (974)
Raw Matching Recurrence Rates Model Fitting Fishergate Site A 8:00 9:00 recurrence rate 25/6/01 26/6/01 27/6/01 28/6/01 29/6/01 25/6/01 1168 (1055) 461 (354) 455 (345) 461 (347) 434 (323) 26/6/01 484 (371) 1149 (1042) 521 (411) 534 (420) 443 (332) 27/6/01 467 (355) 511 (403) 1186 (1076) 528 (414) 457 (346) 28/6/01 455 (342) 503 (395) 508 (398) 1183 (1069) 471 (359) 29/6/01 438 (325) 427 (319) 449 (339) 480 (366) 1159 (1048) 2/7/01 480 (367) 440 (333) 440 (330) 459 (346) 433 (322) 3/7/01 441 (329) 499 (391) 466 (356) 491 (377) 433 (322) 4/7/01 408 (296) 425 (318) 497 (387) 465 (351) 433 (321) 5/7/01 427 (314) 431 (324) 440 (330) 511 (397) 401 (290) 6/7/01 385 (272) 421 (313) 410 (301) 436 (322) 445 (334) 11/7/01 391 (279) 406 (298) 469 (359) 434 (320) 377 (265) 12/7/01 375 (263) 411 (304) 413 (304) 447 (333) 380 (268) 13/7/01 352 (240) 353 (246) 370 (260) 367 (254) 409 (297) 16/7/01 432 (320) 388 (281) 417 (308) 410 (296) 374 (263) 2/7/01 3/7/01 4/7/01 5/7/01 6/7/01 25/6/01 467 (357) 355 (264) 343 (248) 347 (255) 321 (227) 26/6/01 449 (340) 420 (330) 374 (280) 367 (276) 367 (274) 27/6/01 440 (330) 385 (294) 428 (334) 367 (276) 351 (258) 28/6/01 442 (332) 390 (299) 386 (291) 411 (319) 359 (265) 29/6/01 425 (316) 351 (261) 366 (272) 329 (238) 374 (280) 2/7/01 1126 (1016) 445 (354) 426 (331) 397 (305) 377 (283)
Raw Matching Recurrence Rates Model Fitting Fishergate Site A 8:20 8:40 vs entire sample rec rate 25/6/01 26/6/01 27/6/01 28/6/01 29/6/01 25/6/01 1237 (1077) 575 (422) 558 (403) 554 (391) 520 (362) 26/6/01 547 (388) 1160 (1007) 610 (455) 626 (463) 514 (355) 27/6/01 549 (389) 553 (400) 1166 (1011) 642 (479) 542 (384) 28/6/01 563 (403) 592 (438) 610 (455) 1305 (1142) 523 (364) 29/6/01 541 (381) 486 (332) 539 (384) 578 (415) 1152 (994) 2/7/01 562 (402) 551 (398) 540 (385) 577 (414) 527 (369) 3/7/01 506 (347) 610 (457) 559 (405) 590 (427) 519 (361) 4/7/01 500 (340) 547 (394) 562 (407) 589 (426) 485 (327) 5/7/01 504 (344) 496 (343) 504 (349) 610 (447) 468 (309) 6/7/01 445 (285) 514 (361) 509 (354) 524 (361) 527 (369) 11/7/01 441 (282) 497 (344) 545 (390) 569 (406) 460 (302) 12/7/01 439 (279) 464 (310) 486 (331) 528 (365) 427 (269) 13/7/01 427 (268) 396 (243) 463 (308) 467 (304) 454 (295) 16/7/01 504 (344) 444 (291) 469 (314) 489 (326) 414 (256) 2/7/01 3/7/01 4/7/01 5/7/01 6/7/01 25/6/01 581 (422) 469 (336) 444 (308) 469 (338) 455 (321) 26/6/01 547 (388) 514 (380) 448 (313) 441 (310) 435 (301) 27/6/01 542 (383) 483 (349) 497 (361) 456 (325) 438 (304) 28/6/01 515 (356) 495 (362) 474 (338) 517 (386) 443 (309) 29/6/01 514 (355) 453 (319) 442 (306) 402 (271) 455 (321) 2/7/01 1176 (1016) 564 (430) 529 (394) 453 (322) 473 (340)
The General Linear Model Raw Matching Recurrence Rates Model Fitting Hypothesised GLM The data suggests the following GLM E [R] = β 0 + β 1 d + β 2 I w + β 3 I d Where R is the corrected recurrence rate between the two days β i are the model parameters d is the number of days (ex weekends) between the two I w is one if the days are in different weeks I d is one if the days are the same day of the week
Raw Matching Recurrence Rates Model Fitting GLM fitting with highest recurrence rate Site β 0 β 1 β 2 β 3 Ra 2 p-value A 422 (01%) -0800 (01%) -335 (1%) 541 (01%) 0545 173 10 15 B 246 (01%) -0476 (low) -340 (low) 00966 (low) 00225 0198 C 376 (01%) -0510 (01%) -300 (5%) 439 (01%) 0386 679 10 10 D 374 (01%) -0780 (01%) -235 (10%) 518 (01%) 0556 132 10 11 E 535 (01%) -0731 (01%) -536 (01%) 290 (1%) 0644 < 22 10 16 F 342 (01%) -0597 (01%) -246 (low) 201 (low) 0242 536 10 6 G 401 (01%) -100 (01%) -432 (1%) 511 (01%) 0614 618 10 16 H 255 (01%) -0360 (1%) -123 (low) 335 (1%) 0203 0000180 I 359 (01%) -0831 (01%) -323 (1%) 370 (1%) 0540 1361 10 15 J 392 (01%) -0412 (1%) -541 (01%) 249 (10%) 0389 127 10 8 K 427 (01%) -0719 (01%) -487 (01%) 349 (1%) 0636 < 22 10 16 All * 390 (01%) -0666 (01%) -371 (01%) 372 (01%) 0222 < 22 10 16
(1) Note that while the original study was intended Not only does the make up of traffic vary considerably from day to day but the recurrence rate drops off very quickly The combined model shows a recurrence rate of 39% falling off at around 07% per day Obviously this model can only be considered as valid for more than he few weeks being considered Days which are in different weeks differ suffer a reduced recurrence rate (37%) Days which are on the same day of the week have an increased recurrence rate (37%)
(2) Some sites have a considerably higher recurrence rates than others No pattern has yet been determined in why some sites have a higher recurrence rate or whether this is a long-term feature of the sites or a feature of the specific time surveyed If we want to accurately model a traffic system we must account for how quickly the vehicles in the system are being replaced At the moment this work is relying on only data from York more data sets will be analysed soon (more data is welcome)
Bibliograpy Outline 1) This talk online at wwwrichardcleggorg/pubs/ 2) Clegg(2004) The Statistics of Dynamic Networks PhD Thesis Dept of Maths University of York Online at: wwwrichardcleggorg/pubs/thesispdf 3) Clegg and Batley(2001) Driver route Choice and Departure time Choice: The Models and the Evidence Presented at UTSG 2001 Available online at wwwrichardcleggorg/pubs/utsg2001doc 4) Huff and Hanson (1986) Repetition and variability in urban travel Geographical Analysis, 18(2) pp 97 114 5) Pendyala (2003) Measuring day-to-day variability in travel behavior using GPS data Report for Federal Highway Administration Available online at: wwwfhwadotgov/ohim/gps/indexhtml