Traffc State Estmaton n the Traffc Management Center of Berln Authors: Peter Vortsch, PTV AG, Stumpfstrasse, D-763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.vortsch@ptv.de Peter Möhl, PTV AG, Stumpfstrasse, D-763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.moehl@ptv.de Abstract In 999 the development of the traffc management center for the cty of Berln started. The basc dea was to collect traffc data from a number of detecton devces and use that nformaton to provde a set of servces such as dynamc routng n the nternet. Traffc state estmaton s one of the prmary tasks n the traffc management center. Measurement values are avalable only for a fracton of all the lnks n the road network, and for the major part of the network volumes and speeds have to be estmated based on these measurements. A common approach to ths problem s to ft the result of a traffc assgnment to the measurement values by adaptng lnk mpedance or travel demand. In the presented applcaton, a dfferent way was chosen by separatng the estmaton of route choce and travel demand and the estmaton of volumes on the lnks, and perform the computaton for dfferent tme horzons. Onlne route choce estmaton was based on the Path Flow Estmator by Bell supported by an offlne analyss of hstorcal detector data to calbrate demand matrces as good startng solutons. Onlne volume estmaton s performed by a propagaton algorthm where the estmated routng nformaton s used to dstrbute detector values all over the road network. Traffc volumes and speeds are propagated separately. The propagaton method reles on the fact, that the traffc volume observed at a detector s combned from a the flows of a set of paths that spread out n the network before and after the detected lnk. If that path bundle for a measured volume s known, the portons of the sngle flows can be dstrbuted n the road network along ther paths. Snce propagaton becomes less accurate the more turnng movements are ncorporated, a relablty value s computed that decreases as dstance from the measurement locaton ncreases. The method presented s mplemented n the traffc management center and the qualty of the estmaton s assessed by performng a hold-ofsample-test. Keywords: traffc management, traffc state estmaton, traffc forecast, assgnment, measurement 3299 words, 7 fgures TRB 23 Annual Meetng CD-ROM
THE TRAFFIC MANAGEMENT CENTER OF BERLIN In 999 the development of the traffc management center for the cty of Berln started. The basc dea was to collect traffc data from a number of detecton devces and use that nformaton to provde a set of servces such as dynamc routng n the nternet. The senate of Berln contracted a prvate consortum to buld and operate the traffc management center. A system archtecture was chosen that dvded the whole system n the so called content platform provdng nformaton about the current and future traffc stuaton and the servce platform that provded the servces based on the content nformaton to the users. The paper presented wll descrbe the algorthms used n the content platform to estmate and forecast traffc states from local detector nformaton. To measure current traffc flows, about 2 dedcated above-ground detectors were nstalled. These detectors measure volumes and speeds and report them to the center va a GSM cell phone connecton. Snce power s suppled by solar panels and thus naturally lmted, a maxmum number of about transmssons per day s possble. Therefore, an event-drven transmsson algorthm s used,.e. the detector transmts new data f t detects a sgnfcant change n the measured values. In addton, a number of loop detectors on the motorways around and n Berln can be accessed. The network model used n the algorthms conssts of about, lnks representng the major road network n Berln. Travel demand s known from plannng applcatons as orgn-demand matrces referrng to 5 zones. Demand nformaton was gven for separately for the mornng and afternoon peek perod and for the rest of the day for weekdays. Network and demand were avalable n the form of a valdated model n the VI- SUM transport modelng software. Fgure shows the network model and the postons of the detectors. The sold lnes represent the roads for whch level of servce shall be delvered. The dotted lnes are roads that are n the model and used n the computaton, but where no level of servce estmaton s requred. FIGURE : Network model of Berln and detector postons. TRB 23 Annual Meetng CD-ROM
TRAFFIC STATE ESTIMATION General approach Traffc state estmaton s one of the prmary tasks n traffc management centers, snce knowng the actual stuaton s the bass for all nformaton and control applcatons. The Berln stuaton, where about 2 detectors are avalable for a network of several thousand lnks, s rather typcal: measurement values are avalable only for a fracton of all the lnks n the road network, and for the major part of the network volumes and speeds have to be estmated based on these measurements. It s obvous that the estmaton qualty can be mproved f addtonal nformaton s consdered, and the most mportant source of nformaton s the knowledge from the offlne transport plannng process. A well establshed approach to the estmaton problem s to ft the result of a traffc assgnment to the measurement values by adaptng lnk mpedance or travel demand for selected relatons. A well known example s the Path Flow Estmator presented by Bell (). In ths class of estmaton methods traffc assgnment s part of a numercal optmzaton procedure, what means that t s appled teratvely many tmes durng one traffc state computaton. Snce traffc management centers operate under real tme condtons, computaton of the traffc assgnment has to be fast. As a result, the methods n practcal use for the tme beng are restrcted to use smple, statc assgnment procedures, as t s the case wth the path flow estmator. But a statc assgnment procedure s by prncple not capable of modelng short-term dynamc effects n traffc flow, what s requred n traffc state estmaton for control purposes. Only a dynamc assgnment method (e.g. see (2)) s able to handle these effects, but the use of dynamc assgnment wthn an teratve adaptaton procedure has stll to make ts way from academc research to practcal applcatons, at least not for networks of the sze consdered here. Therefore, a dfferent way was chosen to approach the problem by separatng the estmaton of route choce and travel demand and the estmaton of volumes on the lnks, and perform the computaton for dfferent tme horzons. Snce statc assgnment procedures should be used for path estmaton, the tme horzon therefore must not be sgnfcantly smaller than the average (or even more strctly the maxmum) trp duraton n the consdered network. In Berln, a sensble path estmaton perod of hour was assumed. To reflect the current traffc condton n terms of volumes and travel tme on the lnks, a much shorter tme perod, namely fve mnutes, was requred by the servce platform applcatons. To model the short term traffc condtons, the measurement values from the detectors were propagated along the estmated paths every fve mnutes. Behnd ths approach stands the assumpton that route choce n the overall network wll not change as rapdly as the actual volumes on the lnks. The path flow estmaton method can n prncple deduce a demand matrx from detectors values from scratch, but due to the many degrees of freedom path flow estmaton gves much more relable results f an exstng matrx s provded as a startng soluton. Therefore for each hour of each day of the week one demand matrx was deduced offlne by calbratng the gven matrx from transport plannng usng hstorcal measurement values from the last few months. Havng ths set of calbrated hourly matrces t s also possble to use the system wthout the path flow estmator by applyng the propagaton method on the bass of the offlne calbrated matrces. Then however, sgnfcant changes n the real world route choce, e.g. caused by an accdent, are not reflected by the system and wll result n based traffc state estmaton. Fgure 2 shows an overvew, how the offlne matrx calbraton, the onlne path flow estmaton and the onlne measurement propagaton work together to produce estmated speeds and volumes on the network lnks. The followng chapters descrbe the matrx calbraton process and the propagaton procedure. For a descrpton of the path flow estmator, the reader s asked to refer to (). TRB 23 Annual Meetng CD-ROM
Detector Values hstorc, last months last hour last 5 mnutes Matrx- Calbraton (TFlowFuzzy) Path Flow Estmaton (every hour) Measurement- Propagaton (every 5 mn) volumes, speeds am 2 am 3 am 4 am 5 am 6 am 7 am 8 am 9 am am am pm 2 pm 3 pm 4 pm 5 pm 6 pm 7 pm 8 pm 9 pm pm pm 2 pm precomputed assgnments for hour each FIGURE 2: Combnaton of offlne, md-term-onlne and short-term-onlne estmaton procedures Offlne calbraton of traffc assgnments Wthout any onlne detector values, the best estmaton of the traffc stuaton s gven by an assgnment of the best estmaton of the demand matrx for the network model at the gven pont n tme. The measurement propagaton method descrbed below uses the nformaton from such an assgnment and adds the onlne detector nformaton. Therefore t s crucal for the qualty of the overall state estmaton to have relable demand nformaton n a hgh temporal resoluton. The avalable demand matrces from transport plannng covered tme perods of 3 hours for mornng and afternoon peek perods, and there was one more matrx for the rest of the day. For weekend days no demand nformaton was avalable. The detector measurements of the past four months were analyzed to fnd representatves for all days of the week. The frst step was to mutually compare all days of the same type. In order to compare two days, the correlaton was computed for the detector values of all 24 hours of the day separately. These 24 values consst what could be called a correlaton profle of the two days. In fgure 3 sx examples of such profles for some pars of Tuesdays are shown. Day and day 2 are very smlar, whereas day and day obvously have a dfferent mornng peek hour, and so on. The profles were used to select a set of smlar and normal days, and a representatve day was generated by averagng the detector values of the days n that set..8.6.4.2 day : day 2 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23.8.6.4.2 day 2 : day 3 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23.8.6.4.2 day : day 3 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23.8.6.4.2 day 2 : day 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23.8.6.4.2 day : day 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23.8.6.4.2 day 6 : day 8 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23 FIGURE 3: Correlaton profles of several Tuesdays Then for each hour of each representatve day a demand matrx was calbrated based on an equlbrum assgnment. Therefore the matrx calbraton method TFlowFuzzy was appled to the old plannng matrx and the detector values of that hour of the representatve day. TFlowFuzzy s essentally based on an entrope maxmza- TRB 23 Annual Meetng CD-ROM
tector values of that hour of the representatve day. TFlowFuzzy s essentally based on an entrope maxmzaton algorthm, but uses a fuzzy logc approach to deal wth the fact that detector values are not to be taken exact but always contan some randomness. A descrpton of the method s contaned n (3). The calbraton can not make the volumes resultng from the assgned matrx ft exactly the detector values but brngs the values closer together. Fgure 4 shows for some hour the relatonshp between assgned and measured volumes before and after the applcaton of TflowFuzzy. Obvously the methods works well n the area of lower volumes but s not able to brng n some of the hgher volume data ponts. 8 8 7 7 measured volume [veh/h] 6 5 4 3 2 measured volumes [veh/h] 6 5 4 3 2 2 3 4 5 6 7 8 assgnment volumes before TFlowFuzzy 2 3 4 5 6 7 8 assgnment volumes after TFlowFuzzy FIGURE 4: Hourly assgnments wth and wthout calbraton by hstorc measurement values Propagaton of traffc volumes The propagaton method reles on the fact that the traffc volume observed at a detector s combned from a the flows of a set of paths that spread out n the network before and after the detected lnk. If that path bundle for a measured volume s known, the portons of the sngle flows can be dstrbuted n the road network along ther paths. In other words, from a measured volume of vehcles and the knowledge, that 3% of all vehcles wll turn rght at the next juncton, the concluson s that 3 vehcles from the detected volume wll contrbute to the volume on the lnk leavng the next juncton to the rght. Every detector can dstrbute ts flows over the network, and for all lnks the estmated total volume s the sum off all these propagated flows. Snce propagaton becomes less accurate the more turnng movements are ncorporated, a relablty value s computed that decreases as dstance from the measurement locaton ncreases. Ths relablty value can be used to resolve conflcts from competng propagaton results on a lnk. The procedure makes use of the knowledge about the paths that come across the measured lnk. That nformaton s usually the result of a traffc assgnment computaton. However, for applcaton of the propagaton t makes n prncple no dfference whether the route nformaton comes from off-lne transportaton plannng or s estmated on-lne usng an estmaton method lke the path flow estmator. Traffc volumes and speeds are propagated separately. Propagaton of volumes s more powerful, because t s not restrcted by dfferent speed regulatons n the network, and because volume s usually detected n more places than speed. Ths secton covers volume propagaton, the followng one speed propagaton. Step : Downstream propagaton Let q d be the volume measured at detector d. Startng from each detector d n the set of all detectors D each path that comes across the detected lnk s followed downstream and on all lnks n that path ts part q d of the volume q d s stored. For each q d the correspondng value of relablty z d s also stored. The relablty value depends on the dstance and the number of nodes between lnk and detector d. Relablty values are scaled to the nterval [..]. Ther computaton s explaned n more detal n a later secton. TRB 23 Annual Meetng CD-ROM
Step 2: Summng up For each lnk the volume q v estmated by downstream propagaton s the sum of the contrbutons from all detectors: v = q q, d d D Snce the detectors have dfferent dstances from the lnk, the relablty of ther contrbutons s dfferent as well. The relablty z v of the estmated total volume of the lnk s computed as average of the partal relabltes weghted by the volumes: v z = q d z v,, d q d D Step 3: Downstream propagaton and summng up As n step the detector values are propagated along the path bundle, but ths tme upstream. Relablty values are computed n the analogous way and stored at the lnks. Then the propagated values are summed up as n step 2 and for the resultng total volume the correspondng relablty s computed. The result of step 3 s the estmated volume upstream q r and the correspondng relablty z r for all lnks. Step 4: Combnaton of upstream and downstream propagaton results For each lnk two estmatons for volume are computed, one by upstream and one by downstream propagaton. The two values wll n general be dfferent. As fnal estmaton q of the volume the average of the two values, weghted by ther relabltes, s used: q v v r r = ( z q z q ) v r z + z + In a smlar way the total relablty s computed as the volume-weghted average of upstream and downstream relabltes. The followng fgure 5 llustrates the upstream and downstream propagaton of two detector values M and M2. On the lnk between M2 and M2 the propagated values meet and have to be combned consderng ther relablty values. 5 % M 2 % 5 % 8 % M2 FIGURE 5: Upstream and downstream measurement propagaton Computaton of the relablty of the propagated nformaton All volume and speed values used n the propagaton have an assocated relablty value wthn a range between to. By defnton, the relablty of the measured value s. at the lnk where the detector s located. The farther a lnk s away from the detector, the less relable s the part of the detector s total volume propagated to the lnk. The decrease n relablty s descrbed by a functon consderng both pure dstance and the number of possble turnng movements at the nodes between consdered lnk and detector: z = exp α β Length( ) + a L L Wth : TRB 23 Annual Meetng CD-ROM
α β a L z calbraton parameter weght of dstance compared to weght of a node number of possble turnng movements at the end of lnk set of lnks between detector and the consdered lnk resultng relablty on the consdered lnk If a flow falls below a user defned threshold durng propagaton along a path, t s not followed further. A smlar threshold exsts for relablty,.e. a value wth an assocated relablty below the threshold s not consdered any further n computng averages. The followng fgure 6 shows as an example the relablty of the propagated values for a certan detector confguraton. Red denotes low relablty, yellow medum and green hgh relablty. The fgure shows a result obtaned usng a steep decrease functon,.e. the values are consdered relable only n the drect neghborhood of detectors. FIGURE 6: Color-coded relablty for propagated measurement values Propagaton of speed The speeds measured at the detectors are propagated along the road network usng a smlar algorthm, where speed s not propagated drectly, but the rato of measured speed and free flow speed. The reason to do ths s the fact that speed s restrcted by traffc regulatons dfferently all over the network. It would not make much sense to propagate the hgh speeds from a freeway along the urban arterals. There s no summng up step for speeds, they are averaged drectly weghted by relablty. Because propagaton of speed makes sense only wthn smlar road types, e.g. from one freeway secton to the next or wthn an nner-urban area, the lnks are classfed for speed propagaton. Propagaton of a speed value from a detector along one of the paths s ended f a road class change s detected. Extensons of the method If t s not assured that all paths n the network cross at least one detector, t s sensble to set default values for all lnks by usng the results of a traffc assgnment. The relablty of these default values s consdered low. These default values wll be taken nto account n the combnaton of up- and downstream values n step 4 of the procedure descrbed above n the same way as the propagated values. In the neghborhood of detectors the default values wll not nfluence the result heavly because of ther low relablty ratng, but n areas of the network wthout detecton the result of the assgnment values wll be provded as the best estmaton of the traffc stuaton. TRB 23 Annual Meetng CD-ROM
Besdes measurement values from detectors the propagaton method can as well make use of travel demand nformaton n the form of orgn-destnaton-matrces. That s done by defnng vrtual detector values at the zone connecton ponts n the network. In order not to mpose too strct condtons to the overall estmaton, these demand related detector values should have a relablty ratng of less than. It s generally possble to ntegrate further sources of nformaton through the weghted averagng n the combnaton step n the propagaton procedure, and to model the confdence n these sources by the relablty values. An mportant smplfcaton contaned n the method s that the propagaton speed s neglected,.e. the speed at whch traffc flows s not consdered, or even more exactly speakng the shockwave speed up- and downstream the detectors s not consdered. For urban networks wth hgh densty of detectors that smplfcaton s less mportant, but for freeway networks t mght be a sgnfcant mprovement to make the method more dynamc by takng nto account travel tmes between the detector locatons. QUALITY ASSESSMENT OF THE TRAFFIC STATE ESTIMATION The most approprate method to assess the qualty of any traffc state estmaton procedure s, of course, to compare ts results to the actual real-world traffc state. Ths, however, requres addtonal observaton. For example, t s planned to compare estmated level of servce n Berln wth level of servce recorded by human observers. Ths method s not always practcable for assessments durng development and calbraton of the algorthms, a more automatc procedure s needed. Therefore the common approach was adopted to systematcally omt some of the nstalled detectors n the estmaton process and compare ther measured values to the estmated values at the postons of the omtted detectors. It should be kept n mnd that ths s n a way a worst case scenaro, because f the detector postons have been chosen optmally so that they provde maxmum nformaton, these postons are nversely the most hard to estmate wthout a detector. To get an overall qualty ndex, each sngle detector n turn was omtted once and the estmaton procedure was appled for tme slces of one hour. Then the correlaton was computed of all the measured values and the estmated values as explaned n the chapter about the offlne calbraton of the assgnment. Snce level of servce s the fnal objectve, not only the volumes on the lnks are used but also the degree of saturaton of the lnks defned as the volume to capacty rato. The capacty values are taken from the transport plannng model and thus do not reflect the maxmum volume that a lnk can carry at all but the maxmum volume a lnk can carry whle stll provdng satsfactory level of servce. For a randomly chosen normal Tuesday, the results are shown n the followng dagram. The correlaton for the hour from 7 am to 8 am s.93 for the volumes and.78 for saturaton. The traffc state nformaton s publshed n the servce platform usng 3 levels of servce. If the followng smple saturaton based defnton of level of servce s assumed: LOS below 8 % saturaton, LOS 2 between 8 and % saturaton and LOS 3 above % saturaton, then for 7% of the detecton postons the correct level of servce s estmated, 26 % are off by and 4 % are off by two n the example, what would be an acceptable result. TRB 23 Annual Meetng CD-ROM
Estmated volumes [veh/h] 8 7 6 5 4 3 2 2 3 4 5 6 7 8 measured volume [veh/h], Feb. 2 22, 7-8 a.m. Estmated saturaton.5.4.3.2..9.8.7.6.5.4.3.2....2.3.4.5.6.7.8.9...2.3.4.5 Measured saturaton, Feb. 2 22, 7-8 a.m. FIGURE 7: Measured vs. Estmated volumes and degree of saturaton for all detecton ponts REFERENCES. Bell, M.G.H.; Grosso, S.: The Path Flow Estmator as a network observer. Traffc Engneerng & Control Oct. 998, pp. 54-549. 2. Fredrch, M., Hofsäß, I., Nökel, K., Vortsch, P.: A Dynamc Traffc Assgnment Method for Plannng and Telematc Applcatons, Proceedngs of Semnar K, European Transport Conference, Cambrdge, 2. 3. Fredrch, M., Mott, P., Nökel, K.: Keepng Passenger Surveys up-to-date A Fuzzy Approach; presented at the 79th Annual Meetng of the TRB, Washngton, 2. TRB 23 Annual Meetng CD-ROM