Traffic Management Applications of Neural Networks

Transcription

1 Frm: AAAI Technical Reprt WS Cmpilatin cpyright 1993, AAAI ( All rights reserved. Traffic Management Applicatins f Neural Netwrks Jhn F. Gilmre and Khalid J. Elibiary Cmputer Science and Infrmatin Technlgy Lab Gergia Tech Research Institute Gergia Institute f Technlgy Atlanta, Gergia Nahik Abe Mitsubishi Heavy Industries, LTD Nagya Guidance & Prpulsin Systems Aichi-Ken, Japan Abstract Advance Traffic Management Systems (ATMS) must be able t respnd t existing and predicted traffic cnditins if they are t address the demands f the 1990 s. Artificial intelligence and neural netwrk are prmising technlgies that prvide intelligent, adaptive perfrmance in a variety f applicatin dmains. This paper describes tw separate neural netwrk systems that have been develped fr integratin int a ATMS blackbard architecture [Gilmre et al., 1993a]. The first system is an adaptive traffic signal light cntrller based upn the Hpfield neural netwrk mdel, while the secnd system is a backprpagatin mdel trained t predict urban traffic cngestin. Each f these mdels are presented in detail with results attained utilizing a discrete traffic simulatin shwn t illustrate their perfrmance. 1 Intrductin It has been estimated that American drivers annually spend ver tw billin hurs in traffic jams resulting in an estimated $80 billin lss t the U.S. ecnmy. With this ttal expected t grw five fld by the year 2010 and annual traffic fatalities in the United States exceeding 35,000, the develpment f advanced traffic management systems has becme a majr initiative in transprtatin agencies arund the wrld. The gal f an ATMS is t ptimally managexisting transprtatin resurces thrugh the use f adaptive cntrl systems in rder t maximize the efficiency and usefulness f all transprtatin mdes. The intelligent, adaptive cntrl aspects f this prblem are attuned t the features f neural netwrk systems. Neural netwrks [Andersn et al., 1988] are cmputatinal structures that mdel simple bilgical prcesses usually assciated with the human brain. Adaptable and trainable, they are massively parallel systems capable f learning frm psitive and negative reinfrcement. The basic element in a neural netwrk is the neurn (Figure 1). Neurns receive input pulses (1+) frm intercnnectins with ther neurns in the netwrk. These intercnnectins are weighted (W+) based upn their cntributin t the neurn. Weighted intercnnectins are summed internally t the neurn and cmpared t a threshld value. If the threshld value is exceeded, a binary utput pulse (O+) is transmitted, therwise the neurn exhibits n utput value. A variety f specialized neural netwrk mdels based upn this simple neurn structure have been develped ~ Ol W3 I~02 This paper describes the applicatin f neural netwrk t tw ATMS functins. First, an intelligent neural netwrk-base signal light cntrl system capable f 85

2 adaptively ptimizing traffic flw in urban areas is presented. Secnd, a neural netwrk mdel capable f learning hw t accurately predict traffic cngestin is discussed. Current signal cntrl systems, such as the Ls Angeles Autmated Traffic Surveillance and Cntrl (ATSAC), use respnsive cntrl [Rwe, 1991]. cmparing actual surveillance data t available mdel data, a timing plan is selected. This apprach is an imprvement ver the time-f-day timing plan in instances where traffic varies each day. The prpsed neural netwrk apprach extends the ATSAC philsphy further by applying a neural netwrk ptimizatin mdel t actual traffic flw data t determine the signal light settings that will prduce the mst efficient traffic flw in a special event area. Utilizing infrmatin n street segment capacities, traffic flw rates, and ptential flw capacities, the netwrk mdel examines the effects f signal light settings in relatin t the traffic flw away frm a designated area. The system "settles" n cntrl settings that maximize the flw and adaptively changes the signal settings based upn changes in street segment traffic density. Current develpments in advanced traffic cntrl techniques are giving rise t an increasing requirement fr reliable near-future frecasts f traffic flw. These predictins are required in rder t attain the backgrund infrmatin fr slving traffic cngestin befre it develps using methdsuch as "gating" r "dynamic rute guidance". Existing systems such as SCOOT [Rbertsn et al., ~ 1991] nly react t present traffic patterns and, by themselves, d nt prevent cngestin frm ccurring. Cnventinal traffic mdeling and simulatin prcedures can be applied t this prblem but have a number f shrtcmings, particularly in real-time applicatins. Many researchers have demnstrated that neural netwrk methds based n a back-prpagatin algrithm are able t deal with cmplicated nnlinear frecasting tasks in stck prices, electricity demand, and water supply [Canu et al., 1990]. By specifying input values representing imprtantraffic cngestin attributes, a neural netwrk architecture capable f capturing the underlying characteristics f the transprtatin dmain has been develped. This neural netwrk mdel is able t learn based upn data frm previus cngestin ccurences and has prduced encuraging results in frecasting cngestin n surface streets. 2 Traffic Signal Light Cntrller At first glance, a traffic flw system appears t be an interwven and cnnected array f rad sectins whse traffic flw is determined by a series f traffic lights. The cntrl f these traffic lights is vital in rder t allw traffic t flw thrughut the system with minimal delay. A neural netwrk apprach t the cntrl f signals at traffic intersectins is prpsed. Because the ptimal traffic signal cnfiguratin is nt available a priri, a supervised learning architectu re such as a back-prpagatin netwrk is nt suitable. The neural net architecture shuld d unsupervised leaming in an ptimizatin netwrk. The Hpfield neural netwrk mdel was chsen because f its match t the traffic signal cntrl prblem. The main parameter in Hpfield is the energy functin which is distributively defined by the cnnectin architecture amng the neurns and the weights assigned t each cnnectin. The Hpfield mdel and the 2.1 The Hpfield Mdel The Hpfield mdel is an additive neural netwrk mdel. This means that the individual weighted inputs t a neurn are added tgether t determine the ttal activatin f neurn. This activatin is then passed thrugh an utput functin t determine an utput value. traffic-derived energy functin it utilizes fr intelligent signal light cntrl are described in the fllwing subsectins. The Hpfield mdel uses a fully intercnnected netwrkf neurnstdescendnt an energy functin. Since a discrete time simulatin is being used, a discrete-time mdel was adpted. The dynamics f the discrete-time Hpfield Net are given by: iv U i =.i ~1 Ti,jV j d- I i v, = g(u,) 86

3 where T(I,j) are the intercnnectin weights, I(i) are the input biases, U(i) are the internal states, V(i) are the neurn utputs, and g(x) is a nnlinear activatin functin which can taken as which appraches a hard limiter as X tends t zer. An asynchrnus update rule was used which means that neurns are randmly chsen t be updated. This asynchrnus updating scheme tends t greatly reduce scillatry r wandering behavir typical f synchrnus updating schemes. Hpfield and Tank [Hpfield et al., 1984 and 1985] shw that the dynamics f this mdel favrs state transitins that minimize the energy functin where 1 N N N E =-~- )-. Y, T~ j.v~vj- Z IiV/ ~i=lj=l i=l Ti, j are the intercnnectin weights, Vs are the neurn utputs, Ii are the input biases, and N is the number f signals, s that the netwrk gradually settles int a minima f this functin. The difficulty t any applicatin using a Hpfield Net is t determine a suitable energy functin that the netwrk will descend n. 2.2 Neural Signal Cntrller The gal f traffic management is t maximize the flw f traffic while minimizing incidents and delays in aregin. Cntrlling the timing f signals t increase traffic flw is ne methd f supprting this gal. The management f traffic flw by a system utilizing the cntrl f signals appears t directly map int a Hpfield netwrk. Since traffic lights have tw states, each traffic signal can be mdeled as an individual neurn (V0 in a Hpfield neural netwrk. If a light is n, the traffic will flw in the E-W directin at that intersectin, therwise traffic flws in the N-S directin. I, can be viewed as the input ptential int a nde f the netwrk with T~, i viewed as the cnnectins between traffic lights. The first step in any applicatin f the Hpfield netwrk is the cnstructin f an energy functin. The system s primary bjective is t disperse traffic away frm a special event in the shrtest amunt f time. In an abstract sense, ne methd f dispersing traffic is t rute vehicles frm rad segments cntaining a large number f vehicles and a high capacity percentage (vehicle/capacity) nt rad segments with a smaller number f vehicles and a lwer capacity percentage. This can be achieved by [a] changing signal lights based n the ptential f a given traffic light t increase flw, and [b] synchrnizing signals with adjacent traffic lights t maximize verall system thrughput. Initial attempts at creating an energy functin that addresses these criteria cncentrated n examining the number f vehicles n radways t determine ptimal signal light cnfiguratins. Experimentatin sn indicated that the percentage f the capacity f an incming radway was a better indicatr fr determining the state f any given traffic signal. Research int the integratin f rad capacity percentages int the energy equatin was then undertaken. First, a rad segment nearing its capacity will trigger a signal t turn n. Secnd, ptimal flw tends t favr near capacity rad sectins directing their vehicles nt rad sectins with a lwer percentage f capacity. Because f this, a lk at the difference f percentages was adpted. The ptential f a given signal fr traffic flw culd be determined by adding the differences between the traffic capacity percentages int the signal and the percentages f capacity f the flw away frm the intersectin. Thus, the netwrk tends t turn traffic lights n when they have a higher ptential fr large traffic flw. 87

4 -% 1 Dbj,c II II C 8 P! l t I Pririty Time On Figure 2. Traffic Signal Cntrl Energy Functin Derivatin The next step in develping the energy equatin was t addressignal light synchrnizatin. If a signal is n, adjacent signals shuld tend t turn n t further increase traffic flw. A term was added t the energy functin t reflect this tendency f an adjacent traffic light t turn green based n the ptential f adjacent traffic. With this additin, the final energy functin specifying the ptimal cntrl f the traffic lights in the simulatin was defined as: where N (" "~(" p. M L,:~ Ll+t~)t, s:~ J,:l, J N is the number f traffic lights, M & L are the # f utging radways, P(/) is the pririty f a traffic light t(i) is the time that traffic light i has been n, C(b) is the capacity percent f rad sectin D(a)(b(j)) is the difference cap(a)-cap(b(j)), Ill is the utput f neurn i representing traffic light i, r/ is the % f vehicles turning frm a nt b(j), Sk is the % f vehicles turning frm b(j) nt c(k). The numeratr f the term P,/(1 +t,) prvides a priritizatin weight f individual traffic lights in the simulatin, while the denminatr negatively weights traffic lights that have been n fr a lng time. The energy functin tends t favr signal lights with large capacities flwing thrugh their intersectins. The next term f the energy equatin favrs lights whic have high ptential flw ut f the intersectin and int the next light. The final prtin f the energy equatin addresses the cnnectin between secndary signals by measuring their cntributin t the verall primary signals ptential traffic flw. If ne signal is n, the equatin tends adjust signals t als settle int n states. A symblic representatin f energy functin cmpnents is illustrated in Figure Results The graphical interface displays the current traffic flws, capacities, and ptentials fr each street segment n a high reslutin clr mnitr fr viewing by the user. Figure 3. is an example f the neural netwrk traffic signal cntrller display fr the Gergia Dme and Omni sprts arenas. Nrth, suth and east f the Dme and the Omni are the parking lts fr spectatrs attending arena events. Each lt has a number indicating the number f vehicles currently in the lt. Fr example, the lt nrth f the Dme currently cntains 757 vehicles. Traffic data was generated using a discrete traffic simulatr [Hmburger, 1982] f dwntwn Atlanta. This area was selected because it is the site fr the 1996 Summer Olympics and presents the mst challenging traffic management prblem the United States will witness 88

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6 in the 1990 s. The ttal number f vehicles n each street segment is als indicated by a numeric value with the tp number indicating traffic flw t the right and the bttm. nu mber traffic flwing t the left. A single number indicates a ne way street. Street lights are designated by a dash in an intersectin with the flw f traffic (e.g., the green light) mving the same directin as the dash. Fr example, the signal light at the intersectin f Internatinal and Techwd is currently green n Internatinal, but red n Internatinal at its intersectin with Spring Street. The clck in the tp right hand crner displays the actual travel time the simulatin has been running (e.g. ne minutes in this example). Figure 4. indicates the flw f traffic after ten minutes f driving time. This example has assumed that the nly traffic flw in the area was frm the arena parking lts. This was dne t illustrate multiple venue traffic flw interactin. The figure shws that within ten minutes after the Dme and Omni events have ended traffic is efficiently being disbursed. The graphical user interface has been designed t prvide transprtatin engineers with several levels f abstractin during system peratin. Figure 5. is a display f a larger area f dwntwn Atlanta, but with nly primary streets indicated. The Fultn Cunty Stadium area previusly shwn can be seen in less detail in the bttm right prtin f this figure. ATMS peratrs may select the granularity f display they wish t view based upn their current interests. 3 Traffic Cngestin Frecasting An ATMS must nt nly cntrl current traffic, but als predict where cngestin will ccur. Predicting cngestin s that preventive actins may be taken in advance will greatly alleviate traffic gridlcks. This sectin describes the results achieved utilizing a back-prpagatin neural netwrk algrithm t predict the traffic flw n surface street in metrplitan areas. The neural netwrk is trained in tw phases. First, an initial learning phase determines the mst apprpriate cnnecting weights fr data n a typical business day. Secnd, adaptive learning is emplyed t learn the special case traffic classes and adapthe weights t the present situatin. In the adaptive learning phase, the errr functin is cmputed by placing a restrictin n the weight changes that the knwledge learned thrugh the initial learning phase is retained. The prttype system is tested thrugh cmputer simulatins, with results indicating that the applicatin f the neural netwrks t traffic cngestin frecasting is prmising. 3.1 Neural Netwrk Fr Frecasting A multi-layered netwrk cnsisting f three cmpletely cnnected layers (i.e. the input layer, the hidden layer, and the uter layer) was develped t address the traffic frecasting prblem. The learning was achieved using a back-prpagatin algrithm with a sigmid transfer functin. This functin was very suitable t the traffic prblem as traffic flws always pssess a saturatin characteristic. The number f input neurns used in the initial prttype netwrk was 48. These were cmpsed f the target flw (T in Figure 6) and three inflws int the simulated area (11, 12, and Is) which are clsely relevant the target flw. Each variable was nrmalized t [0,1] by using the capacity percentage f the rad fr the target flw and the maximum values f bservedata fr inflws, respectively. It shuld be nted that all data was sampled every 5 minutes, thugh time sampling in the systems is variable. The utputs are target flws in the next 30 minute perid, thus 6 neurns are required. Althugh there is much difficulty in determining the number f neurns fr the hidden layer, 12 neurns were chsen withut any effrt fr ptimizatin in this study. The frecasting algrithm cntains tw phases. First, the learning phase is used t cmpute the ptimal weights f the neural netwrk fr a typical pattern. The secnd is an adaptive frecasting phase t adapt the weights t the presentraffic flws and frecast future cngestin. The training data cnsisted f traffic flw histries frm a typical business day, and the netwrk cnnecting weights were cmputed by fllwing the standard backprpagatin learning rule described belw: 90

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9 3.2 Results where 1 ~(gt - 0,) 2 Y, = t h desired utput Ot = t h actual utput Once the initial learning is cmpleted, the netwrk is ready fr the adaptive and frecasting prcess. The cnnecting weights are crrected accrding t the frecasting errr f the last few data thrugh backprpagatin. In rder t retain the knwledge learned in the initial learning phase, an errr functin with a term t suppress changes f weights was implemented: where E 2 =I ~(y,-,) 12 -(Wii-W, ~ W i = initial weight E =E+kE ~ AW~,~ = maximum value f I Wii - W J i I In additin, a shifting learning methd was used t take the latest available data int accunt. The netwrk was adapted t data fr the past 2 hurs, and wuld then frecasttrafficflwfrthe next hur. Inthe learningperid, all f utputs crrespnding t input data (up t the last 30 minutes) are available fr training data. A prtin f the utputs crrespnding t input data fr the last 30 minutes, hwever, are nt available. This apprach adapted all the weights t the training data (except fr the last 30 minutes) and nly the weights between the available utputs and the hidden layer t the training data frm the last 30 minutes. After the adaptatin prcess, a traffic flw frecast fr the next 30 minutes is generated. The data described abve was used fr the initial learning. In rder t generate test data, randm fluctuatins (+20%) were added t the inflw traffic patterns shwn in Figure 7, and randm fluctuatins were als added t splitting rates f all flws. Figure 8 shws traffic patterns as the simulatin results. Three frecasting criteria, PAAE, standar deviatin f abslute errr, and PITP, were used t evaluate the system perfrmance [Srirengan et el., 1991]. PAAE (Percentage Average Abslute Errr) and standard deviatin f abslute errr are calculated as PAAE = (l/n) Y. I Yt -O, I /(target range)*lo0 t STDEV = ~/(1/N)~( IYt-O, I-(1/N)Y,, I Yt-O, I )2 where nte that target range is equal t 1 and therefre PAAE is equivalent t O/N) T. I y,-, I. t PITP (Percentage f Incrrect Turning Pints) is the percentage f times the predictin f the system is an increase (r decrease) in a perid when in the actual result is the ppsite. Three cases (as shwn in Figure 9.) were tested fr cmparisn: the case withut the adaptive learning (Case 1 ), the case with the adaptive learning using the standard errr functin (Case 2), and the case with the adaptive learning using the prpsed errr functin (Case 3). In all instances, the crrect trend was frecasted in mre than 85% f the time fr the test set. Althugh the frecast accuracy between Cases 1 and 2 did nt always imprve, it was clearly always imprved in Case 3. This indicates that the errr functin was successful in guiding the netwrk s adaptive learning. In additin, it appears that the frecast accuracy f the next 5 minutes is superir and frecast f the next 30 minutes is prest in all cases. This is because the data fr the next 5 minutes has a strnger crrelatin with the input data, as cmpared t data fr the next 30 minutes data. 93

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11 4 Summary Tw applicatins f neural netwrks in advance traffic management have been presented. The intelligent traffic signal cntrl has been develped and applied t several special case traffic situatins including the multiple venue traffic cngestin anticipated during the 1996 Olympics in Atlanta. The traffic cngestin frecasting system has shwn prmise in predicting cngestin based upn learning the factrs that cntribute t traffic jams and gridlcks. Develped independently, research is cntinuing t integrate these systems int an ATMS blackbard architecture cntaining additinal subsystems fr incident detectin, emergency vehicle management, ramp metering, and traffic mnitring. In this cnfiguratin results f predicted traffic cngestin wuld be psted t a blackbar data structure. This actin wuld activate the traffic signal cntrl system which wuld attempt t divert traffic frm the predicted cngestin area. A mre detailed interactin f the ATMS blackbard knwledge surces can be fund in [Gilmre et al., 1993a] 5 References Andersn, J.A. and Rsenfeld, E., Editrs, NeurcmDutina: Fundatins f Research, MIT Press, Cambridge, Massachusetts, Canu, S., Sbral, R., and Lengelle, R., "Frmal Neural Netwrk as an Adaptive Mdel fr Water Demand", Internatinal Neural Netwrk Cnference-Paris, July 1990, Vlume 1, p Gilmre, J.F., Elibiary, K.J., and Petersn, R.J., "A Neural Netwrk System Fr Traffic Flw Management", SPIE Applicatins f Artificial Intelligence, Orland, Flrida, April Gilmre, J.F., and Elibiary, K.J., "AI in Advanced Traffic Management Systems", AAAI93 Wrkshp n Intelligent Highway Vehicle Systems, Washingtn, DC, July 1993a. Gilmre, J. F., and Abe, N., "A Neural Netwrk System Fr Traffic Cngestin Frecasting", submitted t Internatinal Neural Netwrk Sciety Cnference, Nagya, Japan, Octber 1993b. Hayer, D.A., and Tamff, P.J., "Future Directins fr Traffic Management Systems", IEEE Transactins n Vehicular Technlgy, February 1991, Vl. 40, N.I. Hmburger, W.S., Transprtatin and Traffi(;: Engineering Handbk. editr, Institute f Transprtatin Engineers, Washingtn, D.C., 1982 Hpfield, J.J., "Neural Netwrks and Physical Systems with Emergent Cllective Cmputatinal Abilities", Prceedings f the Natinal Academy f Sciences, Vlume 79, p , Hpfield, J.J., and Tank, D.W., "Neural Cmputatin f Decisins in Optimizatin Prblems", Bilgical Cybernetics, Vlume 52, Krnhauser, A.L., "Neural Netwrk Lateral Cntrl f Autnmus Highway Vehicles", Vehicle Navigatin and Infrmatin Systems Cnference Prceedings, Dearbrn, Michigan, Octber Rbertsn, D.J., and Brethertn, R.D., "Optimizing Netwrks f Traffic Signals in Real Time - The SCOOT Methd", IEEE Transactins n Vehicular Technlgy, February 1991, Vl. 40, N.1. Rwe, E., "The Ls Angeles Autmated Traffic Surveillance and Cntrl (ATSAC) System", IEEE Transactins n Vehicular Technlgy, February 1991, Vl. 40, N.1. Srirengan, S., and Li, C. K., "On Using Backprpagatin fr Predictin: An Empirical Study", Internatinal Jint Cnference n Neural Netwrks-Singapre, 1991, Vl. 2., p Tank, D.W., and Hpfield, J. J., "Simple Neural Optimizatin Netwrks: An A/D Cnverter, Signal Decisin Circuit, and a Linear Prgramming", IEEE Transactins n Circuits and Systems, v.33 n.5, May