From: AAAI Technical Report WS-93-04. Compilation copyright © 1993, AAAI (www.aaai.org). All rights reserved.
Traffic
ManagementApplications
of Neural Networks
JohnF. Gilmore
andKhalidJ. Elibiary
Computer
Scienceand InformationTechnology
Lab
GeorgiaTechResearch
Institute
GeorgiaInstitute of Technology
Atlanta, Georgia30332
NaohikoAbe
MitsubishiHeavyIndustries,LTD
NagoyaGuidance& PropulsionSystems
Aichi-Ken,Japan
Abstract
usefulnessof all transportation modes.Theintelligent,
adaptivecontrol aspectsof this problem
are attunedto the
features of neural network systems. Neural networks
[Andersonet al., 1988]are computational
structures that
modelsimplebiological processes
usually associatedwith
the humanbrain. Adaptable and trainable, they are
massively parallel systemscapable of learning from
positive andnegativereinforcement.
AdvanceTraffic Management
Systems(ATMS)must
be able to respondto existing andpredictedtraffic conditions if they are to addressthe demands
of the 1990’s.
Artificial intelligence andneural networkare promising
technologiesthat provideintelligent, adaptiveperformancein a variety of application domains.This paper
describestwo separateneural networksystemsthat have
beendevelopedfor integration into a ATMS
blackboard
Thebasic elementin a neural networkis the neuron
architecture[Gilmoreet al., 1993a].Thefirst system
is an
(Figure 1). Neurons
receiveinput pulses(1+) frominteradaptivetraffic signal light controller baseduponthe
Hopfield neural networkmodel,while the secondsystem connectionswith other neuronsin the network. These
interconnections are weighted(W+) basedupon their
is a backpropagation
modeltrained to predict urbantraffic
contribution to the neuron.Weighted
interconnectionsare
congestion.Eachof thesemodelsare presentedin detail
with results attainedutilizing a discretetraffic simulation summed
internally to the neuron and comparedto a
shown
to illustrate their performance.
threshold value. If the threshold value is exceeded,a
binary output pulse (O+) is transmitted, otherwisethe
1 Introduction
neuronexhibits no output value. A variety of specialized
It hasbeenestimatedthat Americandrivers annually
neural network modelsbasedupon this simple neuron
spendovertwobillion hoursin traffic jamsresulting in an
structure havebeendeveloped.
estimated$80billion loss to the U.S. economy.
Withthis
total expected
to growfive fold by the year2010andannual
traffic fatalities in the UnitedStatesexceeding
35,000,the
12
Ol
11~
W3
developmentof advancedtraffic management
systems
I~02
hasbecome
a majorinitiative in transportation agencies
aroundthe world.
Thegoal of an ATMS
is to optimally manage
existing
transportation resourcesthrough the use of adaptive
control systemsin order to maximizethe efficiency and
85
Thispaperdescribesthe application of neural network
to two ATMS
functions. First, an intelligent neural
network-basesignal light control systemcapable of
adaptivelyoptimizingtraffic flow in urbanareasis presented. Second, a neural network model capable of
learning howto accuratelypredict traffic congestionis
discussed.
This neural networkmodelis able to learn basedupon
data from previous congestionoccurencesand has producedencouragingresults in forecasting congestionon
surfacestreets.
Current signal control systems, such as the Los
AngelesAutomatedTraffic Surveillance and Control
(ATSAC),use responsive control [Rowe, 1991].
comparingactual surveillance data to available model
data, a timing plan is selected. This approachis an
improvement
over the time-of-daytiming plan in instances
wheretraffic varies each day. The proposedneural
networkapproachextendsthe ATSAC
philosophy further
by applyinga neuralnetworkoptimizationmodelto actual
traffic flow datato determine
the signallight settingsthat
will produce
the mostefficient traffic flow in a specialevent
area. Utilizing informationon street segment
capacities,
traffic flow rates, andpotentialflow capacities,the network
modelexaminesthe effects of signal light settings in
relation to the traffic flow awayfroma designatedarea.
Thesystem"settles" on control settings that maximize
the
flow and adaptively changesthe signal settings based
uponchanges
in street segment
traffic density.
2 Traffic SignalLight Controller
Manyresearchers have demonstratedthat neural
networkmethodsbasedon a back-propagationalgorithm
are able to deal with complicatednonlinearforecasting
tasksin stockprices, electricity demand,
andwatersupply
[Canuet al., 1990].Byspecifyinginput valuesrepresenting
importanttraffic congestionattributes, a neural network
architecture capableof capturingthe underlyingcharacteristics of the transportationdomain
hasbeendeveloped.
workof neuronstodescendonto
an energyfunction. Since
a discrete time simulationis beingused,a discrete-time
modelwasadopted. Thedynamicsof the discrete-time
HopfieldNet are given by:
At first glance,a traffic flow systemappearsto bean
interwovenand connectedarray of road sections whose
traffic flow is determined
by a seriesof traffic lights. The
controlof thesetraffic lightsis vital in orderto allowtraffic
to flow throughout
the systemwith minimaldelay. A neural
networkapproachto the control of signals at traffic
intersections is proposed.Becausethe optimal traffic
signalconfigurationis not availablea priori, a supervised
learning architectu re suchas a back-propagation
network
is not suitable. Theneural net architecture should do
unsupervisedleaming in an optimization network. The
Hopfield neural networkmodelwaschosenbecauseof its
matchto the traffic signal control problem.
Themainparameter
in Hopfieldis the energyfunction
whichis distributively definedby the connectionarchitecture amongthe neuronsand the weights assignedto
each connection. The Hopfield model and the
Current developmentsin advancedtraffic control
traffic-derived energyfunctionit utilizes for intelligent
techniques
are giving rise to an increasingrequirement
for
signal light control are describedin the following subreliable near-futureforecastsof traffic flow. Thesepredictions are required in order to attain the background sections.
informationfor solvingtraffic congestion
beforeit develops
2.1 The Hopfield Model
using methodssuchas "gating" or "dynamicroute guidTheHopfield modelis an additive neural network
ance". Existing systemssuch as SCOOT
[Robertson et
~
that the individual weightedinputs to
al., 1991]only react to presenttraffic patternsand, by model.This means
themselves,do not prevent congestionfrom occurring.
a neuron are added together to determine the total
Conventionaltraffic modelingandsimulation procedures activation of neuron. This activation is then passed
can be applied to this problembut have a numberof
throughan output function to determinean output value.
shortcomings,
particularly in real-timeapplications.
TheHopfield modelusesa fully interconnectednet-
86
iV
Ui = .i__~1 Ti,jV j d-
v, = g(u,)
Ii
modeled
as an individual neuron(V0 in a Hopfield neural
network.If a light is on, the traffic will flow in the E-W
directionat that intersection,otherwise
traffic flowsin the
N-Sdirection. I, canbe viewedas the input potential into
where
T(I,j) are the interconnection
weights,
I(i) arethe inputbiases,
U(i) are the internalstates,
V(i) are the neuronoutputs, and
g(x) is a nonlinearactivation function whichcan
taken as
a nodeof the networkwith T~,i viewedas the connections
between
traffic lights.
Thefirst stepin anyapplicationof the Hopfieldnetwork
is the construction of an energyfunction. Thesystem’s
primaryobjectiveis to dispersetraffic awayfroma special
of time. In anabstractsense,
whichapproaches
a hard limiter as Xo tends to zero. An eventin the shortestamount
onemethod
of dispersingtraffic is to route vehiclesfrom
asynchronousupdate rule was used which meansthat
road segments
containinga large numberof vehicles and
neurons are randomly chosen to be updated. This
asynchronousupdating scheme
tends to greatly reduce a high capacity percentage(vehicle/capacity) onto road
with a smaller numberof vehicles anda lower
oscillatory or wandering
behaviortypical of synchronous segments
capacity percentage. This can be achieved by [a]
updating schemes.
changingsignal lights basedon the potential of a given
Hopfield and Tank[Hopfield et al., 1984and 1985]
traffic light to increaseflow, and[b] synchronizing
signals
showthat the dynamicsof this modelfavors state transwith adjacenttraffic lights to maximizeoverall system
itions that minimizethe energyfunction
throughput.
N
1 N N
E=-~- )-’. Y, T~j.V~Vj-Z IiV/
~i=lj=l
’
i=l
where
Ti, j are the interconnection
weights,
Vsare the neuronoutputs,
Ii are the input biases,and
N is the number
of signals,
so that the networkgraduallysettles into a minimaof this
function. Thedifficulty to anyapplicationusinga Hopfield
Net is to determinea suitable energyfunction that the
networkwill descendon.
2.2 Neural Signal Controller
Thegoal of traffic management
is to maximize
the flow
of traffic whileminimizingincidentsanddelaysin aregion.
Controllingthe timingof signalsto increasetraffic flow is
one methodof supporting this goal. Themanagement
of
traffic flow by a systemutilizing the control of signals
appearsto directly mapinto a Hopfield network. Since
traffic lights havetwo states, eachtraffic signal canbe
87
Initial attemptsat creating an energyfunction that
addressesthese criteria concentratedon examiningthe
numberof vehicles on roadwaysto determine optimal
signal light configurations. Experimentationsoonindicatedthat the percentage
of the capacity of an incoming
roadway
wasa better indicator for determiningthe state
of anygiventraffic signal. Research
into the integrationof
road capacity percentagesinto the energyequationwas
then undertaken.
First, a roadsegment
nearingits capacitywill trigger
a signal to turn on. Second,optimal flow tendsto favor
nearcapacityroadsectionsdirecting their vehiclesonto
road sections with a lower percentageof capacity.
Because
of this, a look at the difference of percentages
wasadopted.
Thepotentialof a givensignalfor traffic flow
could be determinedby addingthe differences between
the traffic capacity percentages
into the signal andthe
percentages
of capacity of the flow awayfrom the intersection. Thus,the networktendsto turn traffic lights on
whentheyhavea higherpotential for large traffic flow.
-%
1 Dbj,c
II
II
C
8
P!
l÷tI
Priority
TimeOn
Figure 2. Traffic Signal ControlEnergyFunctionDerivation
Thenext step in developingthe energyequationwas
to addresssignal light synchronization.
If a signal is on,
adjacentsignalsshouldtendto turn onto further increase
traffic flow. A term wasaddedto the energyfunction to
reflect this tendency
of anadjacent
traffic light to turn green
basedon the potential of adjacent traffic. With this
addition, the final energyfunction specifyingthe optimal
controlof the traffic lights in the simulation
wasdefinedas:
N
("
"~("
p.
,:~ Ll+t~)t,
M
s:~
L
’J
,:l
, J
intersections.Thenext termof the energyequationfavors
lights whichhavehighpotentialflow out of the intersection
andinto the next light. Thefinal portion of the energy
equation addressesthe connection betweensecondary
signals by measuringtheir contribution to the overall
primarysignalspotential traffic flow. If onesignal is on,
the equationtendsadjust signals to also settle into on
states. A symbolicrepresentation of energy function
components
is illustrated in Figure2.
2.3 Results
where
Thegraphical interface displays the current traffic
flows, capacities, andpotentials for eachstreet segment
ona highresolutioncolor monitorfor viewingby the user.
Figure3. is anexample
of the neuralnetwork
traffic signal
controller display for the GeorgiaDome
andOmnisports
arenas.North, south andeast of the Dome
and the Omni
are the parkinglots for spectatorsattendingarenaevents.
Eachlot hasa numberindicating the numberof vehicles
currentlyin the lot. For example,
the lot north of the Dome
currently contains757vehicles.
Nis the number
of traffic lights,
M& L are the # of outgoingroadways,
P(/)is thepriorityof a traffic light
t(i) is the timethat traffic light i hasbeenon,
C(b) is the capacitypercentof roadsection
D(a)(b(j)) is the differencecap(a)-cap(b(j)),
Ill is theoutputof neuron
i representing
traffic light i,
r/ is the %of vehiclesturningfroma ontob(j),
Skis the %of vehiclesturningfromb(j) ontoc(k).
Thenumerator
of the termP,/(1 +t,) providesa prioritization
weightof individualtraffic lights in the simulation,
whilethe
denominator
negatively weightstraffic lights that have
beenon for a longtime. Theenergyfunctiontendsto favor
signal lights with large capacitiesflowing throughtheir
88
Traffic data wasgeneratedusing a discrete traffic
simulator [Homburger,1982] of downtown
Atlanta. This
area wasselected becauseit is the site for the 1996
Summer
Olympics and presents the most challenging
traffic management
problemthe UnitedStateswill witness
~.~iiiiiiiiiiiiiiiiiiill
iiiiiiii!i!i
iiii!i
89
in the 1990’s.Thetotal number
of vehicleson eachstreet
segment
is also indicatedby a numericvalue with the top
number
indicating traffic flow to the right andthe bottom.
numbertraffic flowingto the left. A singlenumber
indicates
a onewaystreet.
Streetlights are designated
by a dashin anintersection
with the flow of traffic (e.g., the greenlight) moving
in the
samedirection as the dash.For example,
the signal light
at the intersection of International and Techwood
is
currently greenon International, but red on International
at its intersectionwith SpringStreet. Theclockin the top
right handcorner displays the actual travel time the
simulation has beenrunning (e.g. one minutesin this
example).
employed
to learn the special case traffic classesand
adaptthe weightsto the presentsituation. In the adaptive
learningphase,the error function is computed
by placing
a restriction on the weightchanges
so that the knowledge
learnedthroughthe initial learningphaseis retained.The
prototypesystemis tested throughcomputersimulations,
with results indicating that the applicationof the neural
networksto traffic congestionforecastingis promising.
3.1 Neural NetworkFor Forecasting
A multi-layerednetworkconsistingof three completely
connected
layers(i.e. the input layer, the hiddenlayer, and
the outer layer) wasdevelopedto addressthe traffic
forecasting problem.Thelearning wasachievedusing a
Figure4. indicatesthe flow of traffic after ten minutes back-propagation
algorithmwith a sigmoidtransfer funcof driving time. This example
has assumed
that the only tion. Thisfunctionwasverysuitableto the traffic problem
traffic flow in the areawasfromthe arenaparkinglots.
as traffic flowsalwayspossess
a saturationcharacteristic.
This wasdoneto illustrate multiple venuetraffic flow
Thenumberof input neuronsusedin the initial prointeraction. Thefigure shows
that within ten minutesafter
totype network was 48. These were composedof the
the Dome
andOmnieventshaveendedtraffic is efficiently
target flow (T in Figure 6) andthree inflows into the
beingdisbursed.
simulatedarea(11, 12, andIs) whichare closelyrelevant
Thegraphical user interface has beendesignedto
the target flow. Eachvariable wasnormalizedto [0,1] by
providetransportation engineerswith several levels of
using the capacity percentage
of the road for the target
abstractionduringsystemoperation.Figure5. is a display
flow andthe maximum
valuesof observed
data for inflows,
of a larger areaof downtown
Atlanta, but with only primary
respectively.It shouldbe notedthat all data wassampled
streets indicated. TheFulton CountyStadiumarea preevery5 minutes, thoughtime samplingin the systemsis
viously shown
canbeseenin less detail in the bottomright
variable. Theoutputsaretarget flowsin the next30 minute
protion of this figure. ATMS
operators mayselect the
period, thus 6 neuronsare required. Althoughthere is
granularity of display they wishto viewbasedupontheir
muchdifficulty in determiningthe numberof neuronsfor
currentinterests.
the hidden layer, 12 neuronswere chosenwithout any
3 Traffic Congestion
Forecasting
effort for optimization
in this study.
AnATMS
mustnot only control currenttraffic, but also
Theforecastingalgorithmcontainstwo phases.First,
predict wherecongestionwill occur. Predictingcongestion the learning phaseis usedto compute
the optimalweights
so that preventiveactions maybe takenin advancewill
of the neuralnetworkfor a typical pattern. Thesecondis
greatly alleviate traffic gridlocks.This sectiondescribes
an adaptiveforecastingphaseto adaptthe weightsto the
the results achievedutilizing a back-propagation
neural
¯networkalgorithmto predict the traffic flow on surface presenttraffic flows andforecastfuture congestion.
Thetrainingdataconsistedof traffic flow historiesfrom
street in metropolitanareas.Theneuralnetworkis trained
in twophases.First, an initial learningphasedetermines a typical business day, and the network connecting
the mostappropriate connectingweights for data on a
weights werecomputedby following the standardbacktypical business day. Second,adaptive learning is
propagationlearning rule describedbelow:
90
0
-r"
0
3.2 Results
where
1 ~(gt - 20,)
Y,= t’hdesiredoutput
Ot = t ’h actualoutput
Oncethe initial learningis completed,the networkis
ready for the adaptive and forecasting process. The
connectingweightsare correctedaccordingto the forecasting error of the last few data through backpropagation.In order to retain the knowledge
learnedin
the initial learningphase,an error functionwith a termto
suppresschangesof weights wasimplemented:
The data describedabovewasused for the initial
learning. In order to generatetest data, random
fluctuations (+20%)wereaddedto the inflow traffic patterns
shownin Figure 7, and randomfluctuations werealso
added
to splitting rates of all flows. Figure8 shows
traffic
patterns as the simulation results. Threeforecasting
criteria, PAAE,standarddeviation of absoluteerror, and
PITP, were used to evaluate the system performance
[Srirengan et el., 1991]. PAAE(Percentage Average
AbsoluteError) andstandarddeviation of absoluteerror
are calculatedas
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
wherenote that target rangeis equalto 1 andtherefore
PAAE
is equivalent to
O/N)T. I y,- o, I.
E
~ =Eo+kE
where
t
2Eo =I ~(y,-o,)
PITP(Percentageof Incorrect Turning Points) is the
percentageof times the prediction of the systemis an
increase(or decrease)
in a periodwhenin the actualresult
is the opposite.
21 -(Wii-W°,’~
W°i= initial weight
Threecases(as shownin Figure 9.) weretested for
comparison:
the casewithout the adaptivelearning (Case
AW~,~
= maximum
valueof I Wii - W°Ji I
1 ), the casewith the adaptivelearningusingthe standard
error function (Case2), andthe casewith the adaptive
In addition, a shifting learning methodwasused to take
error function(Case3). In all
the latest available data into account.Thenetworkwas learningusingthe proposed
instances,the correct trend wasforecastedin morethan
adaptedto data for the past 2 hours, and wouldthen
forecasttrafficflowforthenext hour. Inthe learningperiod, 85%of the time for the test set. Althoughthe forecast
accuracybetweenCases1 and2 did not alwaysimprove,
all of outputscorresponding
to input data(up to the last
it wasclearly alwaysimprovedin Case3. This indicates
30 minutes)are available for training data. A portion of
the outputs corresponding
to input data for the last 30 that the error function wassuccessful in guiding the
minutes, however, are not available. This approach network’sadaptivelearning. In addition, it appearsthat
of the next5 minutesis superiorand
adapted
all the weightsto the training data(exceptfor the the forecastaccuracy
last 30 minutes)andonly the weightsbetween
the availforecastof the next30minutes
is poorestin all cases.This
is
because
the
data
for
the
next
5 minuteshasa stronger
ableoutputsandthe hiddenlayer to the training data from
the last 30 minutes.After the adaptationprocess,a traffic
correlationwith the input data, as compared
to datafor the
flow forecastfor the next 30 minutesis generated.
next 30 minutesdata.
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4 Summary
Twoapplicationsof neuralnetworksin advance
traffic
management
havebeenpresented.Theintelligent traffic
signal control hasbeendeveloped
andapplied to several
specialcasetraffic situationsincludingthe multiplevenue
traffic congestion
anticipatedduringthe 1996Olympics
in
Atlanta. Thetraffic congestionforecasting systemhas
shownpromise in predicting congestion basedupon
learning the factors that contribute to traffic jamsand
gridlocks.
Gilmore,J. F., andAbe,N., "A NeuralNetworkSystem
For Traffic Congestion
Forecasting",submittedto International Neural NetworkSociety Conference,Nagoya,
Japan, October1993b.
Hayer,D.A., andTamoff,P.J., "FutureDirectionsfor
Traffic Management
Systems", IEEE Transactions on
VehicularTechnology,February1991, Vol. 40, No.I.
Homburger,
W.S.,TransportationandTraffi(;: Engineering Handbook.
editor, Institute of Transportation
Engineers, Washington,D.C., 1982
Developed
independently,researchis continuing to
integrate these systemsinto an ATMS
blackboardarchitecture containing additional subsystems
for incident
detection, emergency vehicle management,ramp
metering,and traffic monitoring. In this configuration
results of predictedtraffic congestion
wouldbe postedto
a blackboarddata structure. This action wouldactivate
the traffic signal control systemwhichwouldattemptto
divert traffic fromthe predictedcongestionarea. A more
detailed interaction of the ATMS
blackboardknowledge
sourcescanbe foundin [Gilmoreet al., 1993a]
Hopfield, J.J., "NeuralNetworks
andPhysicalSystems
with Emergent
Collective Computational
Abilities", Proceedingsof the National Academy
of Sciences, Volume
79, p. 2518-2577,1982.
5 References
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Hopfield, J.J., andTank, D.W., "Neural Computation
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Kornhauser,A.L., "NeuralNetworkLateral Control of
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95