Estimating the Number of Lane Change Maneuvers on Congested Freeway Segments

Transcription

1 Estmatng the umber of Lane Change Maneuvers on Congested Freeway Segments Chao Wang and Benjamn Cofman Abstract It has long been recognzed that lane change maneuvers (LCMs) can nfluence the relatonshps underlyng traffc flow theory or even dsrupt the relatonshps f lane change maneuvers at crtcal locatons are not properly accounted for. However, the research n ths area has been lmted by the fact that currently there s no effcent method to collect the data on the tmes and locatons of LCMs snce t requres both spatal and temporal coverage. Our research seeks to estmate the number of LCMs n a gven tme-space regon n a manner that s compatble wth exstng vehcle detectors. Employng Vehcle Redentfcaton (VRI), matchng a vehcle observaton at one detector staton to the observaton from a same vehcle at another staton, ths work develops a model to estmate the number of enterng vehcles ( ) and the number of extng vehcles ( ) between the trajectores of two redentfed vehcles. In effect, the work promses to allow for a drect estmate of the number of LCMs. Complete trajectory data sets are used to valdate the model snce these data nclude nformaton on all of the LCMs. Although there are some lmtatons and more research s needed, the approach could eventually be used to contnually estmate the number of LCMs from conventonal detector statons; thereby provdng new nsght nto travel patterns between lanes and the assocated mpacts. I. ITRODUCTIO It has long been recognzed that lane change maneuvers (LCMs) can nfluence the relatonshps underlyng traffc flow theory or even dsrupt the relatonshps f lane change maneuvers at crtcal locatons are not properly accounted for. Recent emprcal research by several groups has shown that LCMs are one of the mechansms that reduce capacty at bottlenecks, e.g., [1]. LCMs are also closely related to traffc accdents, e.g., [-3]. Despte the large mpact from LCMs, the research n ths area has been lmted by the fact that currently there s no effcent method to collect data on the tmes and locatons of LCMs. Such measurement requres extensve coverage both spatally and temporally. Most studes that use LCMs from feld data rely on flm or vdeo, and requre labor-ntensve efforts to extract the necessary nformaton. Image processng technologes are startng to help n ths task, but for accurate LCM data the labor demands reman hgh. Meanwhle, recognzng the need to understand LCMs, several researchers have developed lnear models, nonlnear models and stochastc models n an attempt to capture the nterrelatons between traffc condtons and the frequency of LCMs, e.g., [-7]. However, the outputs from these models are coarse and generally n need of large-scale valdaton and calbraton. Our research seeks to estmate the number of LCMs n a gven tme-space regon n a C. Wang s a Graduate Research Assstant n the Department of Cvl and Envronmental Engneerng and Geodetc Scence, at the Oho State Unversty, Columbus, OH, 31 USA (e-mal: wang.73@osu.edu). B. Cofman s an Assocate Professor wth a jont appontment n the Department of Cvl and Envronmental Engneerng and Geodetc Scence; and the Department of Electrcal and Computer Engneerng at the Oho State Unversty, Columbus, OH 31 USA (phone: ; fax: ; e-mal: Cofman.1@OSU.edu).

2 manner that s compatble wth exstng vehcle detectors. Ths work develops a model to estmate the number of enterng vehcles ( ) and the number of extng vehcles ( ) between the trajectores of two non-successve vehcles. The method requres data from conventonal nductve loop detectors,.e., ths method utlzes data collected at dscrete ponts n space to estmate the number of LCMs between the detector statons. Unlke the prevous work on LCMs, ths estmaton employs Vehcle Redentfcaton (VRI), the process of matchng a vehcle observaton at one detector staton to the observaton from a same vehcle at another staton. Based on VRI results, [8] showed an approach to yeld nflow between redentfed vehcles,.e., -, whch s a constrant on the possble values of and utlzed n the present study. As shown heren, an upper bound and lower bound on and can be obtaned and used to estmate and. In effect, the work promses to allow for a drect estmate of the number of LCMs. Complete trajectory data sets are used to valdate the model snce these data nclude nformaton on all of the LCMs. Although there are some lmtatons and more research s needed, the approach could eventually be used to contnually estmate the number of LCMs from conventonal detector statons; thereby provdng new nsght nto travel patterns between lanes and the assocated mpacts. The remander of ths paper s organzed as follows. Frst, the VRI algorthm s brefly revewed n Secton II. ext, the method to estmate the number of LCMs s ntroduced n Secton III. Then the data set used to valdate the proposed method s presented n Secton IV, followed by an llustraton of the proposed method n Secton V. Fnally, n Secton VI the paper closes wth a summary and conclusons. II. BACKGROUD Vehcle Redentfcaton (VRI) can provde nformaton about the tmes when a gven vehcle passed two (or more) locatons, e.g., for vehcle a3 n Fgure 1 n the form that the upstream vehcle observaton at t 1 and the downstream vehcle observaton at t 3 came from the same vehcle. VRI can be used to capture traffc condtons over extended lnks usng conventonal vehcle detecton equpment at dscrete locatons,.e., ponts along the roadway. Dfferent emergng technologes have been appled for VRI, such as vdeo and Automatc Vehcle Identfcaton (AVI); however, the applcaton of such VRI systems typcally requres the deployment of new hardware. Utlzng the exstng nfrastructure, [9] uses vehcle length measurements from exstng loop detector hardware to redentfy vehcles and s modeled n ths study. The basc dea of the algorthm s to match vehcle sequences snce a sequence of vehcle lengths s much more unque than the consttuent measurements and hence provdes more nformaton than the ndvdual vehcle lengths. The algorthm conssts of three basc steps: measure vehcle length, dentfy possble matches, and address mnor lane change maneuvers. When a vehcle passes over a loop detector bured under the pavement, the resultng measurements can be used to estmate the length of the vehcle. However, measurement uncertanty exsts because of resoluton constrants arsng from the relatvely low samplng frequency of 6 Hz. The uncertanty s nversely proportonal to velocty and true vehcle length. So, vehcle length estmate from the loop detector s expressed as a range, nstead of a

3 sngle dscrete value. In the algorthm, vehcles are assgned successve arrval numbers as they pass a detector staton. These numbers are assgned ndependently for each lane at each staton (upstream and downstream). Statons are taken n adjacent pars and lanes are examned ndependent of other lanes beyond the fact that vehcles may enter or leave the subject lane at any ntervenng locaton. A set of possble matches s found for each downstream observaton,.e., the set of feasble upstream observatons s dentfed whose length ranges ntersect that of the gven downstream observaton. The set of possble matches for each downstream vehcle s stored as a row n a matrx. The rows of the matrx are ndexed by downstream vehcle number and the columns are ndexed by the upstream offset,.e., the dfference between the upstream vehcle number and the downstream vehcle number. Thus, n ths matrx, f there were no lane change maneuvers the true matches would all have the same upstream offset and fall n a sngle column snce the upstream and downstream vehcle numbers would ncrease at the same rate. Fndng the true matches s complcated by the fact that lane change maneuvers dsrupt the sequences and cause the true matches to swtch columns, some vehcles do not have true matches, and most rows have many possble but ncorrect matches dstrbuted randomly across the row. Provded LCMs are nfrequent enough that a gven sequence of true (but unknown) matches s much longer than the sequences of ncorrect matches that arse, the true matches can be found by retanng matches that form long sequences. When too many LCMs occur the algorthm stops redentfyng vehcles untl another lengthy sequence s observed. As a result of ths process, the algorthm wll dentfy platoons of vehcles and many nonredentfed vehcles wll pass between such platoons. 1 III. METHOD TO QUATIFY LCMS Consder the hypothetcal example n Fgure 1, showng the tme space dagram n a sngle lane spannng a par of adjacent detector statons, denoted upstream and downstream. The bold lnes labeled from a1 to a6 n the fgure represent sx vehcles that passed both statons and are redentfed by a VRI algorthm such as presented n Secton II. Snce the VRI algorthm matches vehcle platoons, the redentfed vehcles wll tend to fall n sequences of successve vehcles, wth non-redentfed vehcles between them. Fgure 1 shows two sequences of redentfed vehcles, a1 to a3 are n one sequence and a to a6 n another. Between the two sequences are non-redentfed vehcles labeled from b1 to b5, some of whch are not redentfed because they left or entered the subject lane between detector statons whle others smply are not redentfed although they passed both statons n the subject lane. Our research seeks to estmate the number LCMs n the tme-space regon between sequences of redentfed vehcles, that s, between the trajectores of a3 and a n Fgure 1. 1 For detals on one process of fndng the true matches see [9]. The present paper only emulates the redentfcaton results, the detals of the redentfcaton process are not crtcal, and the only key fact s that vehcle redentfcaton s possble n the frst place. 3

4 Dstance a1 a a3 b1 b b a a5 a6 Downstream Staton B A Upstream Staton Legend: C b3 t 1 t 3 b5 t t Tme Trajectores of redentfed vehcles from VRI Trajectores of non-redentfed vehcles from VRI algorthm Fgure 1. Tme space dagram showng the method to quantfy LCMs D Inflow can be estmated as equaton (1) based on the algorthm presented n [8] and the t shown n Fgure 1. nflow( t3, ) = ( d ( d ( t3)) ( u ( t u ( t1)) (1) Where, nflow ( t, t 3 ) s the nflow between the trajectores of two redentfed vehcles that pass the downstream at tme t 3 and t respectvely, d (t) s the arrval (sequental) number of the vehcle that passes the downstream staton at tmet, and u (t) s the arrval (sequental) number of the vehcle that passes the upstream staton at tmet. Inflow s the dfference between and between two successve redentfed vehcles and gven the nflow, the set of possble and s greatly reduced. Fgure shows the set of feasble values when the nflow s 1.

5 5 3 = nflow Fgure. The relatonshp between nflow and feasble LCMs when the nflow s 1 Fgure llustrates that equaton (1) constrans all the possble par-wse solutons to the nteger values, shown wth crcles on the straght lne. Snce nether nor can be negatve, the lower bound for s max(,nflow) and for s max(, nflow). Although reduced from two dmensons to one, the number of possble par-wse solutons s stll nfnte snce there are no upper bounds for and ; but, subject to reasonable constrants upper bounds can be establshed. If no vehcle both enters and leaves the subject lane between the trajectores of two redentfed vehcles, then and are bounded by the number of vehcles to pass the upstream and downstream statons, respectvely, between redentfed platoons. Ths assumpton does not always hold, as some vehcles do pass through lanes quckly. But provded that the number of vehcles makng such pars of LCMs s relatvely small, the assumpton on the upper lmts greatly smplfes the problem wthout omttng the true and par from the feasble regon. For example, consder the nflow between the trajectores of redentfed vehcles a3 and a n Fgure 1. At the upstream staton, there are four undentfed vehcles between a3 and a. Based on the assumpton, these are the only vehcles that can leave the lane between a3 and a, so can be no larger than four. Smlarly, the upper bound of s three because only three vehcles passed downstream between a3 and a. As a result the soluton space of and s fnte based on the constrants, max(, nflow) ( t3, ) d ( d ( t3) 1 (.a) max(, nflow) ( t3, ) u ( t u ( t1) 1 (.b) nflow( t3, ) = ( t3, ( t3, ) (.c) Where, ( t 3, ) s the number of enterng vehcles between the trajectores of two redentfed vehcles that pass the downstream staton at tmet 3 and t respectvely, and ( t 3, ) s the number of extng vehcles between the trajectores of two redentfed vehcles that pass the downstream staton at tmet 3 and t 5

6 respectvely. As the VRI algorthm redentfes more of the passng vehcles (.e., a hgher redentfcaton rate), constrant () wll yeld tghter soluton bounds. For example, f b n Fgure 1 were redentfed, the soluton bounds between b and a are [,] for and [1,1 ] for, whch leads to the true number of LCMs. Smlarly, reducng matchng errors n the VRI algorthm wll also help to mprove the relablty of constrans (). Where and fall wthn constrants () depends on many factors, such as traffc condtons, the presence of on or off ramps, and whether the lane s an nsde lane, mddle lane or outer lane. Identfyng exactly where and fall wthn the constrants s the subject of ongong research. For smplcty n ths proof of concept study we use the md-pont of the bounds as a pont estmate. So, the equatons to estmate the number of LCMs are as follows, 1 ( t3, ) = [max(, nflow) + d ( d ( t3) 1] (3.a) 1 ( t3, ) = [max(, nflow) + u ( t u ( t1) 1] (3.b) From equaton (1), t can be shown that constrant (.c) s met by defnton f equaton (3) s used to estmate and. IV. DATA DESCRIPTIO The present study employs a vehcle trajectory dataset provded by Federal Hghway Admnstraton s (FHWA) ext Generaton SIMulaton (GSIM) project [1]. The prmary reason to employ a vehcle trajectory dataset s that t ncludes the true LCM nformaton, whch wll be compared wth the estmaton from the proposed method. The vehcle trajectory data were collected on a segment of nterstate I-8 just north of Oakland, Calforna between : p.m. and :15 p.m. on Aprl 13, 5. Fgure 3 shows schematc dagram of the study ste. The data were collected usng seven vdeo cameras mounted on a 3-story buldng adjacent to I-8. Vehcle trajectory data were transcrbed from the vdeo data usng a semautomated process that automatcally detected and tracked vehcles from the vdeo mages. The data nclude vehcle length, speed, lateral poston, longtudnal poston, lane dentfcaton, precedng vehcle ID and followng vehcle ID for every 1/1 th of a second. The ste was approxmately 1,65 feet long wth an on-ramp near the start at Powell St. and an off-ramp to Ashby Ave. just downstream of the study area. The segment s congested for the 15 mnutes when the data were collected. The space mean speed across all 6 lanes s 19 mph, rangng from a space mean speed n lane 1 of 3 mph (a hgh occupancy vehcle, HOV, lane) and n lane 6 of 1 mph. 6

7 165 feet feet feet Ashby Ave Off-ramp Powell Street On-ramp Eastbound I-8 1 (HOV) Fgure 3. Schematc of study segment on I-8, not to scale (adapted from [11]) The dataset provded by GSIM [1] also ncludes dual loop detector data. However, the detector statons are located beyond the segment n whch the trajectory data were extracted and the loop detector data s aggregated to 3-seconds, whch s ncompatble wth the VRI algorthm. Ground truth LCM nformaton s crtcal to evaluate the performance of the proposed method to estmate LCMs and such rch trajectory data s one of the few means that can provde such nformaton. As a publcly avalable data set, the vehcle trajectory of GSIM s uncommon due to the dffculty both n achevng an unobstructed vew of a non-trval length of freeway, and more mportantly the extensve labor needed to reduce the data wth suffcent precson. Once these trajectores are n hand, t s easy to establsh vrtual detector statons at fxed ponts along the road and smulate the results of the VRI algorthm. Because the true matches are already known for these data, rather than employng the VRI algorthm from Secton II, for ths study we emulate the algorthm by specfyng whch vehcles are redentfed n a manner consstent wth the performance of the VRI algorthm, as explaned n the followng secton. V. PILOT STUDY BASED O FIELD DATA Because ths plot study seeks to demonstrate the ablty to estmate and and the true matches are known for each vehcle, the analyss emulates the VRI algorthm. Rather than redentfyng vehcles from the vrtual detectors the VRI results were smulated based on the assumpton that all platoons wth sze of three or more wll be redentfed. Ths smplfed process represents a VRI performance better than presently achevable by dual loop detectors, as t elmnates all ncorrect matches and guarantees other matches are found. But the VRI algorthm s not the topc of ths paper and these assumptons elmnate confoundng factors that could otherwse obscure the estmaton results n ths proof of concept work. The vrtual upstream staton was located at feet nto the study segment and the vrtual downstream staton was located at 1, feet. All 6 lanes were studed. The estmaton results for lane four are shown n Fgure. A total of 1 platoons were observed passng both 7

8 detectors n ths lane over the 15 mnute sample, yeldng pars of and. Fgure (a) shows the true number of obtaned from trajectory data, the estmated based on the method presented n Secton III, and ts upper and lower bounds from constrant () for each of these pars (each correspondng to a tme space regon lke ABCD n Fgure 1). Fgure (b) shows the same nformaton for. The sum of all estmatons for wll yeld an estmaton of the total number of enterng vehcles n lane durng the 15 mnutes (from : p.m. to :15 p.m.) between the vrtual upstream and downstream statons. The spkes n Fgure come from the fact that the number of vehcles between two redentfed platoons (e.g., d (t d (t 3 ) n Fgure 1) vares over a large range. Fgure (c-d) show the dfference between the estmated and true value for and for each par of platoons. 35 (a) Enterng vehcle True value Estmaton Bound 35 (b) Extng vehcle True value Estmaton Bound o. of Lane Changes (veh) o. of Lane Changes (veh) Sequental order of estmaton Sequental order of estmaton Estmaton True Value (c) Enterng vehcle Sequental order of estmaton Estmaton True Value (d) Extng vehcle Sequental order of estmaton Fgure. Estmaton of the number of LCMs n lane Fgure shows that n ths case the proposed method provdes a good estmaton of the true number of LCMs. It also ndcates that the upper bound and lower bound defned n Secton III do n fact bound the true values of and. Fgure 5 shows the correspondng plots for lane 3 wth the bounds removed for clarty. In ths case only platoons were observed, yeldng 19 pars of and. ote that three true values of are zero and the correspondng true values of are non-zero, whch 8

9 means that there are only extng vehcles to separate vehcle platoons n the correspondng tme space regon. 18 (a) Enterng vehcle True value Estmaton 18 (b) Extng vehcle True value Estmaton o. of Lane Changes (veh) o. of Lane Changes (veh) Sequental order of estmaton Sequental order of estmaton (c) Enterng vehcle (d) Extng vehcle Estmaton True Value Sequental order of estmaton Estmaton True Value Sequental order of estmaton Fgure 5. Estmaton of the number of LCMs n lane 3 To quantfy and evaluate the dfferences between the true and the estmated values, the followng measures are appled. I ˆ = MAE = 1 I I ˆ MARE = = 1 I (.a) (.b) Where, MAE s the Mean Absolute Error, MARE s the Mean Absolute Relatve Error, ˆ s the th estmaton of or, and 9

10 s the th true number of or. In equaton (.b), when s zero, ˆ and are removed and I s adjusted accordngly. Table 1 shows the estmaton results for all sx lanes from these two performance measures. Table 1. Estmaton results for all lanes lane 1 lane lane 3 lane lane 5 lane 6 lane 3 (HOV) (VRI 5) o. of through vehcle o. of redentfed vehcles Redentfcaton rate 95% 8% 6% 7% 35% 39% 33% Absolute error (MAE) [vehcles] Absolute error (MAE) [vehcles] Relatve error (MARE) 75% 33% 7% 1% 1% 3% 3% Relatve error (MARE) 5% 8% 1% 16% 6% 6% 61% umber of estmatons Increasng the mnmum platoon length to fve vehcles rather than three, the last column of Table 1 shows the estmaton results for lane 3, smulatng a lower redentfcaton rate. Table 1 shows that estmaton results n lane, lane 3 and lane all have MAE wthn 1 vehcle. Some MAREs n these three lanes are hgh because of nfrequent LCMs. Lane 5 also yelds low MARE, though the MAE s hgher. Both MAE and MARE for lane 6 are hgh because of traffc from the on-ramp and to the off-ramp just beyond the study regon. Lane 1 s a HOV lane wth very few LCM and hgh redentfcaton rate, so t s not surprsng to see the hgh MAREs n Lane 1. VI. COCLUSIOS Lane change maneuvers (LCMs) are mportant to traffc flow theory, traffc delays, and safety. However, relatvely lttle research has been done to study LCMs because of the dffculty n collectng LCM data. Feld collecton s tme and labor ntensve, even wth the help of advanced mage processng technology. Prevous research has studed the relaton between traffc condton and frequency of LCMs, but the model output s coarse and generally n need of large-scale valdaton and calbraton. In response to the need for quantfcaton of LCMs, the present study seeks to estmate the number of LCMs between the trajectores of two redentfed vehcles usng the exstng loop detector nfrastructure. The prmary advance of ths work s the fact that t can estmate and whle earler work could only estmate nflow, the dfference between the two parameters. The proposed method emulates an exstng Vehcle Redentfcaton (VRI) algorthm and estmates nflow between two redentfed vehcles. Based on the assumpton that no vehcle wll both enter and leave the studed lane between the trajectores of two redentfed vehcles, an upper and lower bound of and can be obtaned. For smplfcaton n ths proof of concept, the md-pont of the bounds s used as an estmaton of and. The proposed method was valdated usng vehcle trajectory data collected durng congested condtons. Snce no loop detector data were avalable, vrtual detector statons were used and VRI results 1

11 were smulated based on the assumpton that all platoons wth sze of three or more vehcles wll be redentfed. The plot study provded a drect estmate of the number of LCMs wth reasonable accuracy. The present study has some lmtatons, for example, the VRI algorthm was not mplemented because of the lack of loop detector data for the studed segment. Another example s that the md-pont of the upper and lower bound s taken as an estmaton of and, dscountng the nfluence of traffc condtons on the frequency of LCMs. Our group has also studed the mpacts of LCMs on congested freeway segment delays [1], whch has the potental to be used to mprove the estmaton method proposed n ths paper. Although there are some lmtatons and more research s needed, the approach could eventually be used to contnually estmate the number of LCMs from conventonal detector statons; thereby provdng new nsght nto travel patterns between lanes and the mpacts. ACKOWLEDGEMTS Ths materal s based upon work supported n part by the atonal Scence Foundaton under Grant o and by the Calforna PATH (Partners for Advanced Hghways and Transt) Program of the Unversty of Calforna, n cooperaton wth the State of Calforna Busness, Transportaton and Housng Agency, Department of Transportaton. The Contents of ths report reflect the vews of the authors who are responsble for the facts and accuracy of the data and results presented heren. The contents do not necessarly reflect the offcal vews or polces of the State of Calforna. Ths report does not consttute a standard, specfcaton or regulaton. REFERCES [1] Cofman, B., Krshnamurthy, S., and Wang, X., (3), Lane change maneuvers consumng freeway capacty, Proc. of Traffc and Granular Flow 3, October 3, 3, Delft, etherlands, pp [] Golob, T.F., Recker, W, Alvarez, V., (), Safety aspects of freeway weavng sectons, Transportaton Research A, 38(1), pp [3] Golob, T.F., Recker W.W., (3), Relatonshps among urban freeway accdents, traffc flow, weather, and lghtng condtons, Journal of Transportaton Engneerng, Vol. 19, o., pp [] Worrall R. D. and Bullen A.G., (197), An emprcal analyss of lane changng on multple hghways, Hghway Research Record 33, pp [5] Pahl, J., (197), Lane-change frequences n freeway traffc flow. Hghway Research Record 9, pp [6] Sheu J-B., (1999), A stochastc modelng approach to dynamc predcton of sectonwde nter-lane and ntra-lane traffc varables usng pont detector data. Transportaton Research Part A, 33(), pp [7] Chang G.L. and Kao Y.M., (1991), An emprcal nvestgaton of macroscopc lanechangng characterstcs on uncongested multlane freeways. Transportaton Research Part A, 5(6), pp

12 [8] Cofman, B., (3), Estmatng densty and lane nflow on a freeway segment. Transportaton Research Part A, 37(8), pp [9] Cofman, B. and Cassdy, M., (), Vehcle redentfcaton and travel tme measurement on congested freeways. Transportaton Research Part A, 36(1), pp [1] Federal Hghway Admnstraton, (6), ext Generaton Smulaton Communty (GSIM), accessed on ovember 6, 6. [11] Cambrdge Systematcs, Inc., (5), Summary report: GSIM I-8 Data Analyss (: p.m. to :15 p.m.), Techncal report. [1] Cofman, B., Mshalan, R., Wang, C., Krshnamurthy, S., (6), Impacts of lane change maneuvers on congested freeway segment delays: plot study, Transportaton Research Record, o. 1965, pp