Decompong Travel Tme Meaured by Probe-baed Traffc Montorng Sytem to Indvdual Road Segment Correpondng Author Bruce Hellnga PhD PEng Aocate Profeor Dept. of Cvl and Envronmental Engneerng Unverty of Waterloo Waterloo ON Canada N2L 3G bhellnga@uaterloo.ca Pedram Izadpanah PhD Canddate Dept. of Cvl and Envronmental Engneerng Unverty of Waterloo Waterloo ON Canada N2L 3G pzadpan@uaterloo.ca Hroyu Taada PhD Hanhn Expreay Company Lmted 4--3 Kyutaro-mach Chuo-u Oaa-h Oaa 54-0056 Japan htaada@engmal.uaterloo.ca Lpng Fu PhD PEng Aocate Profeor Dept. of Cvl and Envronmental Engneerng Unverty of Waterloo Waterloo ON Canada N2L 3G lfu@uaterloo.ca Reved: Aprl 2 2008 Publhed n Tranportaton Reearch Part C 6 2008 pp. 768 782.
Decompong Travel Tme Meaured by Probe-baed Traffc Montorng Sytem to Indvdual Road Segment Bruce Hellnga Pedram Izadpanah Hroyu Taada and Lpng Fu Key Word: Probe Vehcle; Ln Travel Tme; Moble Phone; Travel Tme Allocaton
2 Abtract In probe-baed traffc montorng ytem traffc condton can be nferred baed on the poton data of a et of perodcally polled probe vehcle. In uch ytem the to conecutve polled poton do not necearly correpond to the end pont of ndvdual ln. Obtanng etmate of travel tme at the ndvdual ln level requre the total traveral tme hch equal to the pollng nterval duraton be decompoed. Th paper preent an algorthm for olvng the problem of decompong the traveral tme to tme taen to travere ndvdual road egment on the route. The propoed algorthm aume mnmal nformaton about the netor namely netor topography.e. ln and node and the free flo peed of each ln. Unle extng determntc method the propoed oluton algorthm defne a lelhood functon that maxmzed to olve for the mot lely travel tme for each road egment on the travered route. The propoed cheme evaluated ung mulated data and compared to a benchmar determntc method. The evaluaton reult ugget that the propoed method outperform the bench mar method and on average mprove the accuracy of the etmated ln travel tme by up to 90%.
3. Introducton Montorng traffc condton over large road netor ha been a gnfcant challenge for many tranportaton authorte due to large captal expendture requred by mot extng traffc montorng technologe. One poble oluton the ue of ytem that are able to anonymouly trac vehcle uch a cellular phone baed traffc montorng ytem Cayford and Ym 2006. Anonymou tracng ytem uch a cellular phone baed traffc montorng ytem are not retrcted to obtanng nformaton from only a et of dedcated vehcle probe. Rather they anonymouly ample from the total populaton of unt. In the cae of cellular phone baed traffc montorng ytem the poton of a ample of the cell phone thn a pecfed geographcal area are traced over tme. Th proce called locaton referencng. The locaton referencng proce uually carred out by the rele carrer th the reultng data contng of a randomly agned probe vehcle dentfcaton number tme tamp and poton. There are a number of technque n the lterature to etmate poton of a cell phone namely Tme Dfference of Arrval Angle of Arrval and Tmng Advance Izadpanah and Hellnga 2007; Lovell 200; Drane and Rzo 998. The data are then tranmtted to a proceng center for dervng nformaton on traffc condton uch a ln travel tme and peed ncdent and queue. Inferrng traffc condton from poton data requre fve tep a follo:. Map matchng 2. Path dentfcaton 3. Probe Flterng 4. Travel tme allocaton 5. Travel tme aggregaton The frt tep of th nference procedure to addre the ue that poton etmate of a vehcle reported by the cellular phone locaton referencng ytem uually contan error due to everal ource ncludng non-lne-of-ght and mult-path propagaton Taada 2006 and
4 therefore may not correpond to the actual poton of the vehcle on the road netor. Conequently t neceary to determne the mot lely poton of the vehcle on the road netor gven the reported locaton. Th proce termed map matchng. When poton are obtaned relatvely nfrequently there may be more than one poble path on the road netor beteen to conecutvely matched poton. Thu t neceary to dentfy the mot lely path taen by the vehcle to travel beteen to conecutve poton. Th proce called path dentfcaton repreent the econd tep. In anonymou tracng ytem uch a cellular phone baed ytem t not non a pror that the unt e.g. cell phone beng ampled.e. for hch locaton etmate have been obtaned actually a vehcle. The cell phone may be tatonary n a buldng or n the poeon of a pedetran on the deal a peron on a bu on a be etc. Conequently t neceary to flter the ampled unt to ue only data from unt n vehcle. Th proce called probe flterng. The travel tme along a path beteen to conecutvely reported locaton mply equal to the dfference beteen the to conecutve reported tme aocated th the to locaton report. Hoever the dentfed vehcle path may cover a partal ln and/or everal ln. Conequently f the goal to derve travel tme of ndvdual ln there a need to allocate the path travel tme to the ndvdual ln and/or partal ln travered by the vehcle. Th fourth tep of the nference procedure called travel tme allocaton. The lat tep n the proce called travel tme aggregaton to combne ln travel tme from ndvdual probe vehcle nto aggregate etmate of the current or more accurately the recent pat average ln travel tme for all vehcle. Th paper focue only on tep 4 - travel tme allocaton and compare performance of to travel tme allocaton cheme. Conequently t doe not conder the magntude and dtrbuton of error aocated th tep 2 or 3. Follong a bref ummary of prevou reearch the problem formally poed a oluton algorthm propoed and a et of performance meaure ntroduced. Fnally the performance of the propoed algorthm compared th the performance of a benchmar method ung mulated data.
5 2. Prevou reearch The maorty of prevou relevant reearch ha focued on the tep of map matchng path dentfcaton and travel tme aggregaton Taada 2006; Fountan and Smth 2004; Cayford 2003; Pyo et al. 200; Bernten and Kornhauer 996. The tep of flterng and travel tme allocaton have receved lttle attenton n the lterature. One reaon for the lac of reearch on thee to problem that they do not are th dedcated probe ytem hch typcally ue onboard GPS th hgh meaurement frequency e.g. on the order of one or more poton meaurement per econd and hgh poton accuracy. Furthermore thee ytem often have onboard dgtal road map databae and computatonal reource for proceng the data onboard the vehcle. Conequently a dedcated probe able to trac t progre along a ln th a temporal reoluton a lo a one econd or le and drectly determne the tme t entered and exted each ln and thu determne ln travel tme drectly. In contrat anonymou tracng ytem may have loer potonng frequency on the order of one readng per mnute larger locaton error and no on-board proceng. A a reult of thee dfference anonymou tracng ytem are able to provde only the reported poton th accompanyng tme tamp to a central data proceng center CDPC. The CDPC ha a dgtal map databae and ue approprate map matchng path dentfcaton and flterng technque to determne hether or not a probe a vehcle. If the probe determned to be a vehcle then the CDPC etmate the vehcle mot lely travered path beteen to conecutve matched poton. Several rele area-de road condton montorng ytem have been developed nto commercal product and are no beng deployed n North Amerca and elehere Izadpanah and Hellnga 2007; ArSage 2006; TIS Holdng 2006; Appled Generc 2004; Cell-Loc 2002. Unfortunately due to the propretary nature of thee commercal ytem there lttle or no detaled nformaton publcly avalable regardng the pecfc model and algorthm ued thn thee ytem or ho ell they perform. Conequently t not poble to compare the performance of the travel tme allocaton model propoed n th paper th the performance of extng commercal ytem. Conventonally travel tme aocated th any probe vehcle traectory can be allocated to the partal ln and/or ln hch conttute the traectory proportonally to dtance free flo peed or free flo travel tme of the egment. If the route travel tme allocated on the ba of
6 the free flo travel tme of ndvdual ln and partal ln then both dtance and free flo peed are multaneouly condered. In th tudy allocaton of travel tme proportonal to free flo travel tme ued a the benchmar method agant hch the performance of the propoed method compared. 3. Travel tme allocaton problem decrpton and oluton algorthm 3.. Netor model Conder a road netor contng of a et of n node N N = {n a } a= 2 n and a et of m ln L L = { l n a n b n a n b N}. Each node a geographcal locaton on the road netor repreentng a netor feature uch a gnalzed or ungnalzed nterecton hape pont dead end of a road egment croal or locaton of a change n the road attrbute. Each node n a can be defned by t to dmenonal coordnate that n a = x a y a. Other feature aocated th the node may be avalable a part of the map databae e.g. traffc control devce uch a traffc gnal or top gn turnng movement retrcton etc. but are not aumed n the propoed model. A ln the repreentaton of a road egment connectng to node. Each ln aumed to be a drected egment of a traght lne n the map databae. Th aumpton enure the feablty of nferrng the complete ln on the ba of the locaton of t end node. It alo aumed that at mot one ln ext from one node to another and vehcle can travere each ln n only one drecton. The ln from node n a to node n b can be defned a a contnuou et of locaton denoted by ln a n b that are located on the lne beteen n a to n b that l n n λ a { n + λn 0 } = λ b a b here λ a locaton parameter that ued to dentfy any locaton on the ln. Th repreentaton convenent becaue ncreang value of λ correpond to the forard movement of vehcle on the ln. It aumed that to attrbute are aocated th each ln namely free flo peed and ln length. The length of the ln may be calculated by tang the Eucldean dtance beteen n a and n b or may be taen drectly from the map databae. Wth free flo peed and ln length the free flo travel tme of th ln can be calculated a the rato of ln length to free-flo peed. Other attrbute uch a number of lane vertcal gradent lane dth etc. may be avalable but are not requred by the propoed model.
7 A ampled moble probe = 2 K perodcally report t locaton Fgure. The locaton reported by moble probe at tme t = 02 denoted a m ~ and defned a ~ t ~ x t ~ y t m =. PLACE FIGURE ABOUT HERE For each reported locaton m ~ the map matchng proce provde an etmate of the true t poton of the moble probe. The etmated locaton for moble probe at tme t defned a xˆ t yˆ t m ˆ t =. The true locaton of the moble probe defned a x t y t m t =. In practce the map matchng proce ntroduce error and m t t ˆ may not be equal to m. Hoever the focu of th paper trctly on the performance of t travel tme allocaton method and therefore the mpact of map matchng error not condered ˆ t.e. t aumed that m = m. Conequently n the follong model development t m t repreent the matched locaton of moble probe at tme t. If the moble probe beng traced a travelng vehcle th t movement contraned by the road netor then the path dentfcaton proce etmate the route traveled by the moble probe beteen to conecutve locaton m t and m t + denoted by r t t and defned a a equence of ln on the road netor { l m t n l n n l n n l n m t } + r t t = a a a a a a + 2 J J J + Note that the frt ln and the lat ln n the route may repreent only a porton of a ln dependng on the tartng and endng locaton of the probe; thee ln are therefore called partal ln. To mplfy our ubequent dcuon the notaton of the path redefned a follo: { l l l l } = { l 0 J } r t t + = 0 J J 2 here J a more conce repreentaton of partal ln l n m t a + For the purpoe of th reearch t aumed that the travered path r t t ha been J. + dentfed by the precedng tep of the traffc montorng ytem and the focu of th reearch
8 therefore on the problem of allocatng the traveral tme.e. t + - t to the ndvdual ln.e. l on the route r t t. + A llutrated n Fgure 2 the tme nterval beteen to conecutve reported locaton can be decompoed nto four conttuent part a follo:. Mnmum travel tme or free-flo travel tme for the etmated route hch nclude free flo travel tme plu the mnmum tranton tme tme requred hen the vehcle movng from one ln to another adacent ln e.g. left turn 2. Stoppng tme 3. Deceleraton and acceleraton tme and 4. Delay due to traffc congeton. PLACE FIGURE 2 ABOUT HERE The free flo travel tme of a ln calculated a the ln length dvded by the free flo peed hch aumed to be avalable from the dgtal road map databae. here: f l n n a b na nb n n l τ f l na nb = 3 S τ : free flo travel tme for complete or partal ln ln a n b f n n S : free flo peed for complete or partal ln ln a n b a b n l : length of complete or partal ln ln a n b a n b b f The length of ln ln a n b l n a n may be calculated by computng the Eucldean dtance beteen n a and n b. The toppng tme denoted a τ for complete or partal ln l reflect the topped l delay caued to the moble probe by traffc control devce. Note t not aumed that detaled nformaton regardng the locaton type and operatng charactertc e.g. gnal tmng plan a b
9 of traffc control devce non and therefore topped tme cannot be drectly etmated ung conventonal nterecton delay etmaton method. Acceleraton and deceleraton tme aumed to be ncluded thn τ hen thee delay are caued by traffc control and thn f l l τ hen caued by geometry. Conequently acceleraton and deceleraton tme not eparately computed. The fnal component of the travel tme the tme aocated th congeton denoted a τ l c. Congeton tme reult hen the moble probe travel at a peed le than the free peed due to the mpedance of other vehcle. Baed on the above defnton route travel tme beteen to reported locaton can be expreed a: t τ 4 J + t = + τ = 0 { f l + τ l c l } Note from Equaton 4 that both τ and τ are unnon and need to be determned l c l eparately before the total travel tme can be allocated to ndvdual ln. The follong ecton decrbe the benchmar and propoed method for calculatng thee to component. 3.2. Benchmar Travel Tme Decompoton Method The benchmar travel tme decompoton method allocate τ and τ.e. travel l l c tme n exce of the free flo travel tme n proporton to the free flo travel tme Equaton 5. τ l t t f t l = J + τ f l q= 0 q Where n Equaton 5 t l τ l + τ l explctly compute τ and τ. l c =. Note that n th method there no need to l c 5
0 3.3. Propoed Travel Tme Decompoton Method The propoed travel tme decompoton method attempt to provde a more accurate allocaton of travel tme by recognzng that vehcle are more lely to ncur toppng delay.e. τ l at the dontream rather than uptream end of a ln epecally hen the ln nfluenced by a traffc control devce. Hoever e aume that detaled nformaton regardng the locaton and operatng charactertc of traffc control devce e.g. traffc gnal not non and therefore t not poble to drectly determne: the fracton of the total route travel tme aocated th topped delay; and 2 here along the route.e. hch ln the probe vehcle experence th topped delay. In the next to ecton e preent a method for over-comng both of thee challenge. 3.3.. Computng Congeton Tme The propoed approach to determnng ln congeton tme baed on the aumpton that the degree of congeton on each of the ln on the route nearly equal. Th aumpton condered to be reaonable hen the number of ln on r t t relatvely mall hch + expected to be the cae hen cellular phone are polled at an nterval of one mnute or le. When traffc demand lo delay due to congeton hould be relatvely mall and therefore mlar. On the other hand hen traffc demand hgh all ln thn cloe proxmty are expected to experence relatvely mlar degree of congeton. Congeton due to unexpected event tend to pread qucly over a number of ln a drver ee alternate route and queue gro. Furthermore probe ll travere feer ln or partal ln thn a pollng nterval a congeton ncreae. We defne a congeton ndex a the rato of the congeton tme on the route to the um of the congeton tme and free peed tme on the route Equaton 6 = J { τ c l } { τ c l + τ f l } = 0 J = 0 6
Ung th defnton the mnmum value of zero and occur hen traffc demand very lo and the probe travel at the free peed. The maxmum value of alay le than. We re-rte Equaton 6 by expreng the tme aocated th congeton along the J r + hch denoted by τ c.e. τ c = { τ c l } route t t congeton ndex and the non free flo travel Equaton 7. = 0 { τ f l } = 0 a a functon of the unnon J τ c = 7 The mnmum value of τ c 0 and occur hen = 0. The maxmum value of τ c occur for the maxmum value of hch occur hen vehcle travel at a peed le than free flo peed due to traffc congeton and experence no delay caued by traffc control devce. Th maxmum value obtaned by ubttutng τ 0 nto Equaton 5 and defned a follo: l = J = t + t { f l } τ max = T τ 8 c c Ung Equaton 7 and 8 the maxmum value of can be determned by = 0 max τ cmax = t t + 9 It not poble to reolve Equaton 7 at th pont becaue τ c a functon of hch unnon. To reolve th ue t further aumed that the degree of congeton on the route travered by the moble probe durng the mot recent pollng nterval not ubtantally dfferent from the degree of congeton experenced on the route travered by th ame moble probe durng the prevou pollng nterval. Baed on th aumpton e ntroduce a model to capture the lelhood that a certan degree of congeton experenced by a moble probe hen traverng a gven ln denoted by P. P = mn t T I c p t + T + t t I + I + p p c 0
2 Where: I p = the larget nteger le than for hch T c I p le than t I p + t I p. Th requrement enure that for the prevou route beng condered the moble probe ha not remaned tatonary for the entre pollng nterval. Equaton 0 tructured to reflect to aumpton: Frt t aumed that hen all other attrbute are held contant the lelhood of a partcular level of congeton occurrng ncreae a the maxmum delay due to congeton.e. T c ncreae. Second t aumed that for a gven maxmum delay due to congeton very hgh level of congeton are le lely than loer level of congeton. Thee to aumpton and the relatonhp defned by Equaton 0 are llutrated n Fgure 3 for to ample cae. For each cae the pollng nterval.e. t + - t aumed to be 30 econd and the maxmum delay due to congeton for the probe route durng the prevou nterval.e. T c I p aumed to be 5 econd. The mpact of aumpton oberved by comparng the value of P for Cae and 2 for a gven value of ay = 0.6. For Cae the maxmum delay due to congeton 5 econd and for Cae 2 5 econd. Gven that all other attrbute beteen the to cae are the ame t expected that the ln n Cae 2 more heavly congeted. Th reflected by the hgher lelhhod for all level of congeton for Cae 2 compared th Cae. The mpact of aumpton 2 reflected n both curve by the decreae n P for ncreang level of congeton. 3.3.2. Computng Stoppng Tme Stoppng tme aocated th the delay experenced a a reult of toppng for a traffc control devce. Hoever t not poble to determne drectly f the moble probe ha topped along the route and f t ha topped here the probe topped and for ho long. Furthermore t aumed that pecfc charactertc of the road netor uch a the locaton of traffc gnal top gn etc are not non and therefore t not poble to develop model that rely on gnal tmng nformaton etc. Neverthele t can be aumed that f a traffc control devce
3 ext on a ln t located at the dontream end of the ln and therefore f a vehcle top on a ln t more lely to do o near the dontream end of the ln than at the uptream end. PLCAE FIGURE 3 ABOUT HERE It alo expected that the queue created by traffc control devce are lely to become larger a the level of congeton ncreae and therefore the lelhood of toppng at a locaton near the uptream end of the ln ncreae a the level of congeton ncreae. The probablty of toppng defned on the ba of the toppng lelhood functon provded n Equaton. p λ h λ = e + C Where: C p = and C and C 2 are model parameter that are ued to reflect the toppng lelhood pattern of a ln. The lelhood a functon of both the poton on the ln λ and the level of congeton and reflect the expectaton that hen a ln experence relatvely lo level of congeton queue formed uptream of traffc control devce are relatvely hort and vehcle that are requred to top a a reult of the queue tend to do o near the dontream end of the ln. Hoever a the ln become ncreangly more congeton queue become longer and the lelhood that a vehcle requred to top farther uptream alo ncreae. A llutrated n Fgure 4 the propoed lelhood functon reflect the mpact of locaton on the ln and level of congeton n a ay that content th traffc engneerng expectaton. Conequently any other functon that behave n the ame manner can be choen a long a the range of the lelhood functon contraned beteen 0 and. The parameter C and C 2 are choen n a ay to enure that the range of the functon beteen 0 and. A entvty analy preented at the end of the paper to clarfy the mportance of thee to parameter on the accuracy of the propoed travel tme allocaton method. PLCAE FIGURE 4 ABOUT HERE 2
4 The probablty of toppng on a ln l hch on the route + t t r can be determned by ntegratng the lelhood functon along the length of the ln: { } C e e p C e p d C e d h l H p p p p 2 2 2 2 2 2 2 2 2 2 2 + = + = + = = λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ 2 If t aumed that a moble probe top at mot once on the route + t t r then the probablty of toppng on ln l J gven by = = othere l H l H J f l H l P J J J 0 0 3 Fnally the etmated toppng tme can be obtaned by ntegratng over the hole range of poble level of congeton on the ln. d Q l P P l J J 0 max = τ τ 4 Where: { } = + = 0 J c f l t t τ τ τ 4b = = max 0 0 J d l P P Q 4c In Equaton 4b τ denote toppng tme for the route + t t r. Then the etmated congeton tme can be obtaned by ntegratng over the hole range of d Q l P P l J J c J J c 0 0 max = = τ δ τ 5
5 Where: δ J = τ l J τ f l = 0 f J 5b Equaton 5 mple that the tme aocated th traffc congeton agned to each ln accordng to the proporton of the mnmum travel tme of the ln to the mnmum travel tme of the route. Fnally t l = τ l + τ l + τ l = 0 2 J 6 f here tl denote travel tme of ln or partal ln n tme nterval t t + hen moble probe traced. c 4. Illutratve example Conder a moble probe that travere a porton of a road netor. The route travered durng tme nterval t t + cont of to partal ln and one complete ln Fgure 5. Aume t + - t = 60 econd. The free flo travel tme.e. τ l of each complete ln f equal to 5 econd. Hoever the moble probe travere only 2/3 of the frt ln and /3 of the lat ln on the route and therefore the free peed travel tme can be determned a 0 5 and 5 econd repectvely. PLACE FIGURE 5 ABOUT HERE On the ba of Equaton 8 T c = 60 0 + 5 + 5 = 30 econd. Aume that the mnmum travel tme for the prevou route travered by the moble probe a greater than zero and therefore I p = -. Aume T c - = 5 econd and t - t - = 90 econd. Conequently P can be computed ung Equaton 0 for each value of e.g. for =0.3 P = 0.78. The probablty of the moble probe toppng on each of the three ln on the route can be computed ung Equaton 2. For example for = 0.3 p = 2.33 C = 0.7 C 2 = 0.5 and for the frt ln on the route λ = /3 λ 2 =.0 and thu
6 H l 0.3 0.3 = 2.33.0 0.333 2.33 2.330.333 e e + 0.50.3 0. 505 0 = Smlarly H l 0.3 = 0.42 and H l 2 0.3 = 0.253. Equaton 3 ued to determne the probablty of toppng on each ln. 0. 3 = H l 0 0. 3 H l 0. 3 H l 2 0. 3 = 0. 505 0. 42 0. 253 P l 0 = 0. 29 Smlarly P l 0.3 = 0.56 and P l 2 0.3 = 0.072. The um of thee probablte = 0.447. From Equaton 7 for = 0.3 τ c = 2.9 econd. From Equaton 4c Q = 0.54 and J the term P P l J n Equaton 5 equal to 0.347. For the frt ln from = 0 Equaton 5b δ 0 = 0/30. From Equaton 8 hen τ c = T c = 30 econd max = 30/60 = 0.5. The calculaton of τ c l 0 completed by ntegratng over all level of beteen 0 and 0.5 a per Equaton 5 reultng n τ c l 0 = 3.63 econd. Smlarly τ c l = 5.44 and τ c l 2 =.8 econd. From Equaton 4b for = 0.3 τ = 7. econd and from Equaton 4 τ l 0 = 9.8 econd. Smlarly τ l = 6.84 and τ l 2 = 2.47 econd. Table tabulate the calculated value for each component of travel tme aocated th each ln. The calculaton aocated th the benchmar method are traghtforard. For example the travel tme aocated th the frt ln =0 equal to the pollng nterval duraton t - t - multpled by the free flo travel tme for the ln dvded by the free flo travel tme for the route 90 0/30 = 20 econd. PLACE TABLE ABOUT HERE
7 5. Performance evaluaton 5.. Evaluaton Netor The performance of the propoed method a evaluated ung a hypothetcal arteral netor hon n Fgure 6. Traffc flo on the netor ere modeled ung the INTEGRATION mcrocopc traffc mulaton model Van Aerde 2002a b. The tet netor compoed of 32 ln 8 node 3 gnalzed nterecton and ungnalzed nterecton. All ln ere agned a free peed of 60 m/h and a aturaton flo rate of 900 paenger car per hour. The netor a mulated for a perod of 25 mnute. Data from the frt 5 mnute of mulaton ere condered to be part of the arm-up perod and ere not ued n the analy. PLACE FIGURE 6 ABOUT HERE Fgure 7 llutrate the ln traveral tme experenced by ndvdual vehcle a a functon of mulaton tme for to ample ln - ln 3 hch controlled by a traffc gnal and ln 3 hch n not controlled by any type of traffc control devce Fgure 6. The reult n the fgure for the ln controlled by the traffc gnal clearly reflect the gnfcant nfluence that the traffc gnal ha on the ln traveral tme. Vehcle that arrve at the nterecton ut a the gnal turn red may experence ln traveral tme that are approxmately 8 tme a large a the traveral tme of vehcle that ncur no gnal delay. In th tudy all generated vehcle are treated a probe vehcle and poton of each probe vehcle are reported at a predefned fxed frequency. It hould be noted that parameter C and C 2 that are ued n Equaton ere aumed to be 0.7 and 0.5 repectvely. PLACE FIGURE 7 ABOUT HERE 5.2. Performance Meaure An obervaton condered to be to conecutve locaton reference for an ndvdual probe vehcle. Each obervaton may be categorzed nto one of three type a llutrated n Fgure 8:. Both of the reported poton le on the ame ln Fgure 8-a 2. The frt and econd reported poton are located on adacent ln Fgure 8-b 3. At leat one full ln ext beteen the to reported poton Fgure 8-c.
8 In the frt cae the vehcle path cont of only a partal ln. In the econd cae the vehcle path cont of to partal ln. In the thrd cae the route beteen the to conecutve reported locaton compoed of a partal ln at both end of the route and at leat one full ln n beteen. For the frt cae the travel tme of the partal ln equal to the pollng nterval of the locaton regardle of the method ued. Hoever th not true for Cae 2 and 3 and therefore for thee Cae the travel allocaton method ued doe have an mpact on the accuracy. PLACE FIGURE 8 ABOUT HERE In th tudy the ln travel tme etmaton error aocated th each partal or full ln for each probe vehcle route determned by comparng the ln or partal ln travel tme etmated by the propoed method and the benchmar method th the correpondng true travel tme a extracted drectly from the mulaton model. The performance of the propoed method and the benchmar quantfed on the ba of to meaure of accuracy. The frt meaure E l n defned n Equaton 7 can be ued to compare the performance of the to travel tme etmaton method at the ndvdual ln level. a n b E n n l a b ATT N r= = l na nb TA TT r N r 2 7 here: E l n : Average normalzed error aocated th travel tme allocaton for ln ln a n b a n b R l n : Obervaton et for ln ln a n b a n b r : Index denote any ndvdual obervaton n R l n n N : Number of obervaton n R l n n a b a b TA r : Allocated travel tme of obervaton r hch calculated baed on ether the propoed or the benchmar travel tme allocaton method
9 TT r : True travel tme of obervaton r. ATT l n a n b : N Average travel tme of all obervaton n R l n a n.e. ATT b l n n = TT a b N The econd meaure E an aggregate meaure of performance and obtaned by averagng the ln level error E l n n etmated ung Equaton 7 over all ln n the netor. a b r= r E = L L E 8 Where: E : Average error for the netor L: Set of all ln n the netor L : Dmenon of the et of all ln L E : The error obtaned for ln ung Equaton 7. 5.3. Reult Fgure 9 depct the relatonhp beteen aggregate travel tme etmaton error E and pollng nterval duraton for both the propoed and benchmar method. A can be een n thee reult the propoed method uperor to the benchmar method for all pollng nterval duraton examned. Furthermore the reult ho that etmaton error mallet for very hort pollng nterval duraton but ncreae rapdly a the pollng nterval duraton ncreae untl a maxmum error plateau reached E 0.75 for the benchmar method at a pollng nterval duraton of 60 econd; E 0.65 for the propoed method at a pollng nterval duraton of 00 econd. The relatve mprovement n etmaton accuracy provded by the propoed method can be computed a B E P E B E here E P and E B are the overall error for the netor obtaned ung the propoed and the benchmar method repectvely. The reult n Fgure 9 ugget that the propoed method provde a reducton n overall etmaton error of approxmately 40% for pollng nterval duraton of 35 and 60 econd. The mprovement are maller for other pollng
20 nterval duraton 25% for a pollng nterval duraton of 5 econd; 4% for 90 econd; and 9% for 00 econd. PLACE FIGURE 9 ABOUT HERE The reult depcted n Fgure 9 can be explaned on the ba of the proporton of Cae Cae 2 and Cae 3 obervaton a per Fgure 8 for each of the pollng nterval duraton. Fgure 0 provde the fracton of obervaton of each type for each dfferent pollng nterval duraton. A expected the fracton of Cae 3 obervaton ncreae a the pollng nterval become larger. Recall that there no error aocated th the travel tme allocaton for Cae obervaton and alo t expected that the travel tme allocaton error for Cae 3 larger than for Cae 2. Conequently overall etmaton error trongly correlated th the proporton of Cae 2 and Cae 3 obervaton and trongly negatvely correlated th the proporton of Cae obervaton. PLACE FIGURE 0 ABOUT HERE It can be oberved n Fgure 9 that for each etmaton method the etmaton error approxmately equal for pollng nterval duraton of 00 econd and 90 econd. In Fgure 0 t can be oberved that for thee to pollng nterval duraton the proporton of Cae 2 and Cae 3 obervaton are very mlar. Nether the propoed method nor the benchmar method aume that nformaton avalable pecfyng the locaton and charactertc of traffc control devce. Hoever t qute clear from the reult provded n Fgure 8 that the ln travel tme charactertc of the ln controlled by a traffc gnal are gnfcantly dfferent from thoe ln that are not controlled by a gnal. Conequently t of nteret to examne the accuracy of the propoed method and the benchmar method for each ln cla eparately. Fgure and 2 depct etmaton error for the propoed and benchmar method repectvely a a functon of ln cla.e. controlled by a traffc gnal or not and the rato of pollng nterval duraton to the free flo travel tme. Th rato ued for the x-ax a t multaneouly capture the mpact of pollng nterval duraton and t mpact on the proporton of Cae Cae 2 and Cae 3 obervaton and ln length hch alo nfluence the proporton of each Cae type. PLACE FIGURE ABOUT HERE
2 PLACE FIGURE 2 ABOUT HERE The follong obervaton can be made from the reult n Fgure and 2:. Etmaton error generally larger for ln not controlled by a traffc gnal than for ln that are controlled by a traffc gnal. The larger error appear to reult from a tendency for the propoed method to over-etmate the tme allocated to the ungnalzed ln. Th obervaton eem to mply that overall etmaton accuracy can be mproved f the locaton of traffc control devce non. 2. A the pollng nterval to free flo travel tme rato ncreae the etmaton error alo ncreae but at a decreang rate. A 2 nd order polynomal regreon of the form E = β + 2 0 + βα β2α a performed on the data from each ln cla eparately. β 0 β and β 2 are the regreon coeffcent; α the rato of pollng nterval duraton to the free peed travel tme of the ln; and E the regreon predcton of the etmaton error. The reultng regreon relatonhp are llutrated n the fgure and th the excepton of the model for the ln not controlled by a traffc gnal for the benchmar method explan a large proporton of the varance exhbted n the data. The coeffcent for each model are provded n Table 2. PLACE TABLE 2 ABOUT HERE 3. The etmaton error for the propoed method are maller than the error from the benchmar method for ln that are controlled by a traffc gnal and ln that are not controlled by a gnal. The relatve mprovement n etmaton accuracy more clearly depcted n Fgure 3 hch llutrate the percent reducton n error provded by the ue of the propoed method for both ln clae. The reducton n etmaton error a computed a Where: EB α = 9 α EP α E α B
22 Δα E B α E P α α : Fractonal reducton n etmaton error provded by the ue of the propoed method for a value of α : Etmaton error a predcted by the approprate regreon model ftted to the data obtaned from ue of the benchmar method for a value of α : Etmaton error a predcted by the approprate regreon model ftted to the data obtaned from ue of the propoed method for a value of α : rato of the pollng nterval duraton to the free peed travel tme for the ln. PLACE FIGURE 3 ABOUT HERE The reult from Fgure 3 ndcate that for a hort pollng nterval duraton or for long ln.e. α mall the propoed method provde a reducton n etmaton error of approxmately 90% for ln that are controlled by a traffc gnal and approxmately 70% for ln not controlled by a traffc gnal. The relatve mprovement provded by the propoed method decreae a the pollng nterval duraton ncreae and/or the ln become horter; hoever over the range of pollng nterval duraton and ln length condered the propoed method uperor to the benchmar method. In Fgure 3 the mprovement provded by the propoed method larger for ln controlled by a traffc gnal untl the rato of pollng nterval duraton to free flo travel tme approache a value of 2. When the rato of pollng nterval duraton to free flo travel tme exceed a value of approxmately 2 the relatve mprovement provded by the propoed method larger for ln not controlled by a traffc gnal. Hoever th reult hould be veed th cauton a t dependent on the regreon model reult and the model for ln not controlled by a traffc gnal for the benchmar ha a relatvely lo R 2 value. 6. Sentvty analy Equaton provde a model hch decrbe toppng lelhood of vehcle along a ln. Accordng to th equaton the toppng lelhood a functon of both poton on the ln λ and the level of congeton. To model parameter denoted by C and C 2 ere ued to reflect the toppng lelhood pattern of the ln. In the prevou ecton of th paper value of C = 0.7 and C 2 = 0.5 ere ued. There ext the ue of ho to elect approprate value and the entvty of the performance of the propoed travel tme allocaton method n term of the average error for the netor E to thee to model parameter.
23 Examnaton of Equaton ho that the toppng lelhood ncreae for larger value of C 2. Furthermore n order to enure that the toppng lelhood functon vare beteen 0 and C 2 mut be retrcted to be beteen 0 and. Converely a C ncreae the toppng lelhood deceae though reman potve and conequently C may tae on any potve value. The entvty of the performance of the propoed travel tme allocaton method to the value of C and C 2 llutrated n Fgure 4. The y-ax repreent the entvty S meaured a S E C C 0.70.5 0.70.5 2 = 20 E E Where: E : Average netor error obtaned from the propoed travel tme allocaton method C C 2 ung parameter value C and C 2. E : Average netor error obtaned from the propoed travel tme allocaton method 0.70.5 ung parameter value C =0.7 and C 2 =0.5. The pollng nterval a held equal to 60 econd. Every ndvdual curve n the fgure aocated th a contant value for C. The reult demontrate that the propoed travel tme allocaton method relatvely nentve to the value of C and C 2. Over the range of value condered n the entvty analy the overall netor error only change by beteen -.7% and 6.6%. The propoed travel tme etmaton method perform better than the benchmar method for all parameter value C and C 2 combnaton condered n the entvty analy. PLACE FIGURE 4 ABOUT HERE 7. Concluon Th reearch addree the problem of travel tme allocaton hch one of the tep requred to obtan average travel tme for ndvdual ln n a road netor on the ba of poton data obtaned from anonymouly traced probe vehcle. In th tudy a method for travel tme allocaton a propoed and the performance of the propoed method a evaluated agant a benchmar ung data from a mulated netor. It a found that the frequency of the locaton referencng and the ln free peed travel tme are mportant factor nfluencng the accuracy of the travel tme etmate.
24 It a oberved that the propoed method mprove the accuracy of the travel tme allocaton by an average of 40% for all ln n the netor for a pollng nterval duraton of 60 econd. Hoever mprovement can be a large a 90% for long ln that are controlled by a traffc gnal. It oberved that the propoed method tend to over etmate the travel tme for ln that are not controlled by a traffc gnal. Conequently f the locaton and type of traffc control devce a aumed to be non not an unreaonable aumpton gven that ome electronc map databae already contan th nformaton then t lely that th nformaton could be ncorporated thn a modfed form of the propoed method n order to mprove the accuracy of the travel tme etmate. It recommended that future reearch effort addre the follong: a develop a travel tme allocaton method that can mae ue of nformaton about the type and locaton of traffc control devce; b quantfy the mportance of travel tme allocaton accuracy on the accuracy of aggregate ln travel tme etmate; c explore method by hch travel tme etmated for partal ln can be ued to etmate aggregate ln travel tme; and d evaluate the propoed method for an actual road netor. Acnoledgement Th reearch a fnancally upported n part by the Natural Scence and Engneerng Reearch Councl of Canada. Reference Cayford R. Ym Y. 2006. A feld operaton tet ung anonymou cell phone tracng for generatng traffc nformaton. The 85 th Annual Meetng of the Tranportaton Reearch Board CD-ROM Wahngton D.C USA. Taada H. 2006. Road traffc condton acquton va moble phone locaton referencng. PhD Dertaton Unverty of Waterloo Ontaro Canada. Bernten C. Kornhauer A.L. 996. An ntroducton to map matchng for peronal navgaton atant. Ne Jerey TIDE Center. Cayford R. 2003. Method and ytem for electroncally determnng dynamc traffc nformaton. Unted State Patent No. 6560532.
25 Pyo J.S. Shn D.H. Sung T.K. 200. Development of a map matchng method ung the multple hypothe technque. Proceedng of IEEE Intellgent Tranportaton Sytem Conference Oaland CA USA. Fountan M.D. Smth B. 2004. Improvng the effectvene of traffc montorng baed on rele locaton technology. Vrgna Tranportaton Reearch Councl Fnal Report VTRC 05- R7. ArSage Company Webte 2006. Acceed from http://.arage.com. Appled Generc Ltd. 2004. RoDIN24 road traffc montor GSM Edton. Acceed from http://.appledgenerc.com. Cell-Loc Inc. 2002. Traffc montorng applcaton of cellular potonng technology: Proof of concept. Acceed from http://.tc.gc.ca/tdc/ummary/3900/3936e.htm. TIS Holdng Company Webte 2006. Acceed from Http://.tholdng.com. Van Aerde M. & Aoc. Ltd 2002a. INTEGRATION RELEASE 2.30 FOR WINDOWS: Uer' Gude Volume I: Fundamental Model Feature. Van Aerde M. & Aoc. Ltd 2002b. INTEGRATION RELEASE 2.30 FOR WINDOWS: Uer' Gude Volume II: Advanced Model Feature. Drane C Rzo C. 998. Potonng ytem n ntellgent tranportaton ytem. Artech Houe INC. ISBN: 0-89006-536-5. Lovell D.J. 200. Accuracy of peed meaurement from cellular phone vehcle locaton ytem. Journal of Intellgent Tranportaton Sytem Vol. 3 p. 303-325. Izadpanah P. Hellnga B. 2007. Wde-area rele traffc condton montorng: realty or hful thnng? Proceedng of Annual Conference of the Canadan Inttute of Tranportaton Engneer Toronto Ontaro.
26 : Ln : Node Fgure : Defnton for vehcle traectory.
27 Ln Ln + Ln +2 Dtance along route Deceleraton Stopped Acceleraton f < f S f = Free Flo Speed S = Speed Ln Ln + Ln +2 Tme Fgure 2: Travel tme component.
28.0 0.9 Probablty of Degree of Congeton Occurng P 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. 0.0 t t I p + + t T I c Cae : T c=5 Cae 2: T c=5 t p I p = 30 = 5 = 30 0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Level of Congeton Fgure 3: Probablty of congeton a a functon of level of congeton.
29.0 0.9 0.8 Stoppng Lelhood hλ 0.7 0.6 0.5 0.4 0.3 0.2 = 0.9 Very hgh congeton = 0.7 = 0.5 = 0.3 0. = 0. very lo congeton 0.0 0.0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9.0 Uptream Dontream Locaton on Ln λ Fgure 4: Stoppng lelhood a a functon of level of congeton and locaton on ln.
30 =0 = =2=J λ= /3 m t τ f 0 5 λ= /3 m t + 5 Fgure 5: Example path of moble probe.
3 Ln3 Ln 3 Fgure 6: A hypothetcal netor to evaluate performance of the propoed method.
32 60 40 Smulaton "Warmup" Perod Ln 3: controlled by traffc gnal Ln 3: no traffc control devce 20 Tme to Travel Ln econd 00 80 60 40 20 0 0 00 200 300 400 500 600 700 800 900 000 00 200 300 400 500 Smulaton Tme of Probe Entry to Ln econd Fgure 7: Varaton of travel tme for to ample ln.
33 a Cae : to reported poton le on the ame ln. : Reported Poton : Netor Node b Cae 2: reported poton are located on adacent ln. c Cae 3: at leat one full ln ext beteen the to conecutve reported poton. Fgure 8: Three dfferent travel tme decompoton cae that can occur.
34 0.80 80% Overall Average Travel Tme Etmaton Error 0.70 0.60 0.50 0.40 0.30 0.20 The Propoed Method The Benchmar Method Improvment n Etmaton Accuracy 70% 60% 50% 40% 30% 20% Improvement n Etmaton Accuracy % 0.0 0% 0.00 0% 0 0 20 30 40 50 60 70 80 90 00 0 Pollng Interval Duraton econd Fgure 9: Overall average travel tme etmaton error E.
35 00% 80% Fracton of Obervaton of Each Cae Type 60% 40% Cae 3 Cae 2 Cae 20% 0% 5 35 60 90 00 Pollng Interval Duraton econd Fgure 0: Fracton of obervaton of each Cae type a a functon of pollng nterval duraton.
36 2.0.8 Ln controlled by traffc gnal Ln not controlled by a traffc gnal.6 Error calculated ung Equaton 7.4.2.0 0.8 0.6 R 2 = 0.8 R 2 = 0.9335 0.4 0.2 0.0 0 2 4 6 8 0 2 4 6 Pollng Interval / Free Flo Travel Tme Fgure : The propoed method etmaton error a a functon of ln cla.
37 2.0.8 Ln controlled by a traffc gnal Ln not controlled by a traffc gnal.6 Error calculated ung Equaton 7.4.2.0 0.8 0.6 R 2 = 0.5596 R 2 = 0.8296 0.4 0.2 0.0 0 2 4 6 8 0 2 4 6 Pollng Interval / Free Flo Travel Tme Fgure 2: The benchmar method etmaton error a a functon of ln cla.
38 00% 90% Ln controlled by a traffc gnal Ln not controlled by a traffc gnal 80% Reducton n Etmaton Error % 70% 60% 50% 40% 30% 20% 0% 0% 0 2 3 4 5 6 7 8 9 0 2 3 4 5 Pollng Interval/Free Flo Travel Tme α Fgure 3: Relatve mprovement n etmaton accuracy provded by the propoed travel tme allocaton method.
39 Sentvty S 8.0% 7.0% 6.0% 5.0% 4.0% 3.0% 2.0%.0% 0.0% -.0% -2.0% -3.0% 0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Value of Parameter C 2 C=0.7 C= C=2 C=3 C=4 C=5 C=6 Fgure 4: Sentvty of average error for the netor E to model parameter C and C 2 for pollng nterval duraton of 60 econd.
40 Table :Sample calculaton. Propoed Method Benchmar Method Ln No. = 0 2 Sum τ f 0.00 5.00 5.00 30.00 τ 9.8 6.84 2.47 9.2 τ c 3.63 5.44.8 0.88 Total 23.44 27.28 9.28 60.00 Total 20.00 30.00 0.00 60.00
4 Table 2:Regreon model coeffcent. Regreon Model Coeffcent Propoed Method Benchmar Method Sgnalzed Not Sgnalzed Sgnalzed Not Sgnalzed β 0 0.0093 0.0592 0.093 0.234 β 0.0782 0.393 0.069 0.523 β 2-0.008-0.0042-0.004-0.005
42 Lt of Fgure Capton Fgure : Defnton for vehcle traectory. Fgure 2: Travel tme component. Fgure 3: Probablty of congeton a a functon of level of congeton. Fgure 4: Stoppng lelhood a a functon of level of congeton and locaton on ln. Fgure 5: Example path of moble probe. Fgure 6: A hypothetcal netor to evaluate performance of the propoed method. Fgure 7: Varaton of travel tme for to ample ln. Fgure 8: Three dfferent travel tme decompoton cae that can occur. Fgure 9: Overall average travel tme etmaton error E. Fgure 0: Fracton of obervaton of each Cae type a a functon of pollng nterval duraton. Fgure : The propoed method etmaton error a a functon of ln cla. Fgure 2: The benchmar method etmaton error a a functon of ln cla. Fgure 3: Relatve mprovement n etmaton accuracy provded by the propoed travel tme allocaton method. Fgure 4: Sentvty of average error for the netor E to model parameter C and C 2 for pollng nterval duraton of 60 econd.
43 Lt of Table Capton Table : Sample calculaton. Table 2: Regreon model coeffcent.