Technische Universität München 1 Traffic Simulation with Queues 09.2008 Ferienakademie, Sarntal...

Technische Universität München 1

Traffic Traffic Simulation Simulation with Queueswith Queues

09.2008

Ferienakademie, Sarntal

Neven Popov

2Technische Universität München

OutlineOutline MotivationMotivation IntroductionIntroduction

Traffic simulationTraffic simulation Two modelsTwo models

Nagel-Schreckenberg modelNagel-Schreckenberg model Cellular automatonCellular automaton Essential stepsEssential steps DisadvategousDisadvategous

Queue modelQueue model Queue data structureQueue data structure Model of Simao and PowellModel of Simao and Powell GawronGawron’s model’s model ExtensionsExtensions Parallel computingParallel computing ResultsResults

Comparison between the two modelsComparison between the two models


MotivationMotivation How to avoid traffic jams?How to avoid traffic jams?

Cities with light traffic?Cities with light traffic? In the USA with the name “Transims” for In the USA with the name “Transims” for

parallel computing parallel computing Basis for the OSLIM-Traffic predictions in Basis for the OSLIM-Traffic predictions in

Nordrhein-WestfalenNordrhein-Westfalen








Introduction – Traffic Introduction – Traffic SimulationSimulation

Microscopic model – through Microscopic model – through description of the decisions of the description of the decisions of the single carssingle cars

Decisions and conditions of the systemDecisions and conditions of the system

Source: http://ebus.informatik.uni-leipzig.de


Introduction – Two Introduction – Two modelsmodels

Nagel-Schreckenberg modelNagel-Schreckenberg model Interactions between the vehiclesInteractions between the vehicles

Four essential stepsFour essential steps

Queue modelQueue model No interactions between the vehiclesNo interactions between the vehicles

Faster movement of the vehiclesFaster movement of the vehicles








Cellular automatonCellular automaton Cellular automatonCellular automaton

Neighborhood conditionsNeighborhood conditions

The condition depends on the previous time The condition depends on the previous time stepstep

Von-Neumann Neighborhood

Moore Neighborhood Source: http://www.wikipedia.orgSource: http://www.wikipedia.org


Cellular automatonCellular automaton

Game of LifeGame of Life

Source: http://www.wikipedia.org


Nagel-Schreckenberg Model - Nagel-Schreckenberg Model - Four Essential StepsFour Essential Steps

Four important stepsFour important steps 1) Acceleration1) Acceleration (if v(if vn,n, < v < vmax max set vset vn n = v= vn n + 1)+ 1)

2) Slowing down2) Slowing down (if sites to n+1-th vehicle (j) <= v(if sites to n+1-th vehicle (j) <= vn n so set so set

vvn n = j-1)= j-1)

3) Randomization3) Randomization (if v(if vn n > 0 so set v> 0 so set vn n = v= vn n – 1 with probability p)– 1 with probability p) 4) Car motion4) Car motion (move the cars with v(move the cars with vnn cells forward) cells forward)

Configuration at time step tConfiguration at time step t

Acceleration with vAcceleration with vmax max = 2= 2

Slowing downSlowing down

Randomization with probability pRandomization with probability p

Car motion (time step t+1)Car motion (time step t+1)

Source: http://ebus.informatik.uni-leipzig.de


Reason for applying Queue Reason for applying Queue modelmodel

Cellular automata too complexCellular automata too complex Too many cells to representToo many cells to represent The behavior of the driver too complexThe behavior of the driver too complex

That’s why :That’s why :

Transition to Queue modelTransition to Queue model Simplifying the Cellular automationSimplifying the Cellular automation More realistic by building of traffic jamsMore realistic by building of traffic jams








QueueQueue Important data structureImportant data structure Access only to the border elementsAccess only to the border elements

Example FIFO-Queue (First In, First Out) Source: http://www.wikipedia.org


Queue modelQueue model Model of Simao and PowellModel of Simao and Powell

Traffic networkTraffic network Nodes (Places)Nodes (Places) Edges (Streets)Edges (Streets)

EdgesEdges In sub edges In sub edges FIFO-QueuesFIFO-Queues Leaving depends on the capacityLeaving depends on the capacity


Gawron’s ModelGawron’s Model

Generating the traffic networkGenerating the traffic network O-D MatricesO-D Matrices

Describe basic movement patterns during a certain Describe basic movement patterns during a certain period of time (e.g. 24 hours)period of time (e.g. 24 hours)

N Vehicles leave origin o in order to get to the destination N Vehicles leave origin o in order to get to the destination d during time td during time t

Origin node -> Destination node = #VehiclesOrigin node -> Destination node = #Vehicles

Iteration for computation of the fastest routeIteration for computation of the fastest route

OriginOrigin DestinatiDestinationon

#Vehicle#Vehicless

00 55 500500

22 1010 3030

77 33 236236

88 9090 3737


Gawron’s ModelGawron’s Model

Computation of the departure timeComputation of the departure time Through laminar trafficThrough laminar traffic Through a preferred speedThrough a preferred speed

Edges have limited spaceEdges have limited space Leaving only if there is a next free edgeLeaving only if there is a next free edge Building of traffic jamsBuilding of traffic jams


Dependency between Dependency between Velocity and DensityVelocity and Density

Laminar Laminar TrafficTraffic

Capacity Capacity dominatidominatingng

CongestiCongestion areaon area

Source: http://www.wikipedia.org


ExtensionsExtensions

However,However, O-D Matrices not realistic enoughO-D Matrices not realistic enough O-D Matrices not flexibleO-D Matrices not flexible It can be achieved even more efficiencyIt can be achieved even more efficiency

Applying of:Applying of: AgentsAgents Event-Driven Queue Based SimulationsEvent-Driven Queue Based Simulations


Modelling of AgentsModelling of Agents Replaces O-D MatrixesReplaces O-D Matrixes Activities of the single personActivities of the single person Building of activities through Building of activities through

iterationsiterations

Plan 1- Home till 9 am- Drive to work (car)- Work 8h, beginapprox 9.30 am-Drive to sports (car)- Sports 19 pm to 22 pm (optional)- Drive home (car)

Plan 2- Home till 8 am- Drive to work (pt)- Work 8h, beginapprox 8.30 am-Drive to sports (pt)- Sports 18 pm to 21 pm (optional)- Drive home (pt)


Event-Driven Queue Based Event-Driven Queue Based SimulationsSimulations

Substitution of the constant time-step Substitution of the constant time-step through direct treatment of actionsthrough direct treatment of actions

Most computational time where traffic Most computational time where traffic flow is maximalflow is maximal

Results :Results : Simulation performance is being boostedSimulation performance is being boosted Advantageous for the parallel computingAdvantageous for the parallel computing Fast simulation of huge traffic networksFast simulation of huge traffic networks


Elements of the Event-Elements of the Event-Driven Queue Based Driven Queue Based

SimulationsSimulations

Activity plan

Agent Road segment

ClockSet timer

Wake up

Entry/arrival time

Register


Results from the Event-Results from the Event-Driven Queue Based Driven Queue Based

SimulationsSimulations

Independent from the size of the Independent from the size of the traffic networktraffic network

Boosting up with factor of ten in Boosting up with factor of ten in comparison to simple Queue modelcomparison to simple Queue model

There is no case where the other There is no case where the other models are fastermodels are faster


Parallel computingParallel computing

Partitioning of the networkPartitioning of the network Every partition to a different processorEvery partition to a different processor

Source: D. Charypar und K.W. Axhausen und K. Nagel, An event-driven parallel queue-basedmicrosimulation for large scale traffic scenarios, VSP Working Paper, 07-03. (2007)


ResultsResults Test cases : Berlin and BrandenburgTest cases : Berlin and Brandenburg

11,6k nodes and 27,7k edges11,6k nodes and 27,7k edges 7,05M simulated persons for 24 hours7,05M simulated persons for 24 hours 249M used edges for 24 hours249M used edges for 24 hours

Used computer systemUsed computer system Shared memory parallel computer with 256GB Shared memory parallel computer with 256GB

RAMRAM 64 dual-core Intel Itanium 2 processors with 1,65 64 dual-core Intel Itanium 2 processors with 1,65

GHzGHz ResultsResults

Boosting up with factor of 53Boosting up with factor of 53 Time for simulation : 87sTime for simulation : 87s


EfficiencyEfficiency Linear factoring to 64 processorsLinear factoring to 64 processors Best result by 4 processorsBest result by 4 processors

Source: D. Charypar und K.W. Axhausen und K. Nagel, An event-driven parallel queue-basedmicrosimulation for large scale traffic scenarios, VSP Working Paper, 07-03. (2007)








Comparison between the Comparison between the two modelstwo models

The Queue model (in general)The Queue model (in general) Higher efficiency Higher efficiency More realism by building of congestionsMore realism by building of congestions

Nagel-Schreckenberg modelNagel-Schreckenberg model A better observation of the interactions A better observation of the interactions

between the vehiclesbetween the vehicles More complex than the Queue modelMore complex than the Queue model


Questions?Questions?

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Technische Universität München 1 Traffic Simulation with Queues 09.2008 Ferienakademie, Sarntal...

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