Traffic Simulation with Queues

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Traffic Simulation with Queues
Ferienakademie, Sarntal Neven
Popov

09.2008
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Outline

• Motivation
• Introduction
• Traffic simulation
• Two models
• Nagel-Schreckenberg model
• Cellular automaton
• Essential steps
• Disadvategous
• Queue model
• Queue data structure
• Model of Simao and Powell
• Gawrons model
• Extensions
• Parallel computing
• Results
• Comparison between the two models

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Motivation

• How to avoid traffic jams?
• Cities with light traffic?
• In the USA with the name Transims for parallel
  computing
• Basis for the OSLIM-Traffic predictions in
  Nordrhein-Westfalen

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Outline

• Motivation
• Introduction
• Traffic simulation
• Two models
• Nagel-Schreckenberg model
• Cellular automaton
• Essential steps
• Disadvategous
• Queue model
• Queue data structure
• Model of Simao and Powell
• Gawrons model
• Extensions
• Parallel computing
• Results
• Comparison between the two models

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Introduction Traffic Simulation

• Microscopic model through description of the
  decisions of the single cars
• Decisions and conditions of the system

Source http//ebus.informatik.uni-leipzig.de
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Introduction Two models

• Nagel-Schreckenberg model
• Interactions between the vehicles
• Four essential steps
• Queue model
• No interactions between the vehicles
• Faster movement of the vehicles

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Outline

• Motivation
• Introduction
• Traffic simulation
• Two models
• Nagel-Schreckenberg model
• Cellular automaton
• Essential steps
• Disadvategous
• Queue model
• Queue data structure
• Model of Simao and Powell
• Gawrons model
• Extensions
• Parallel computing
• Results
• Comparison between the two models

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Cellular automaton

• Cellular automaton
• Neighborhood conditions
• The condition depends on the previous time step

Von-Neumann Neighborhood
Moore Neighborhood
Source http//www.wikipedia.org
Source http//www.wikipedia.org
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Cellular automaton

• Game of Life

Source http//www.wikipedia.org
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Nagel-Schreckenberg Model - Four Essential Steps
Source http//ebus.informatik.uni-leipzig.de

• Four important steps
• 1) Acceleration
• (if vn, lt vmax set vn vn 1)
• 2) Slowing down
• (if sites to n1-th vehicle (j) lt vn so set
• vn j-1)
• 3) Randomization
• (if vn gt 0 so set vn vn 1 with probability
  p)
• 4) Car motion
• (move the cars with vn cells forward)

• Configuration at time step t

• Acceleration with vmax 2

• Slowing down

• Randomization with probability p

• Car motion (time step t1)

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Reason for applying Queue model

• Cellular automata too complex
• Too many cells to represent
• The behavior of the driver too complex
• Thats why
• Transition to Queue model
• Simplifying the Cellular automation
• More realistic by building of traffic jams

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Outline

• Motivation
• Introduction
• Traffic simulation
• Two models
• Nagel-Schreckenberg model
• Cellular automaton
• Essential steps
• Disadvategous
• Queue model
• Queue data structure
• Model of Simao and Powell
• Gawrons model
• Extensions
• Parallel computing
• Results
• Comparison between the two models

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Queue

• Important data structure
• Access only to the border elements

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

• Model of Simao and Powell
• Traffic network
• Nodes (Places)
• Edges (Streets)
• Edges
• In sub edges
• FIFO-Queues
• Leaving depends on the capacity

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Gawrons Model

• Generating the traffic network
• O-D Matrices
• Describe basic movement patterns during a certain
  period of time (e.g. 24 hours)
• N Vehicles leave origin o in order to get to the
  destination d during time t
• Origin node -gt Destination node Vehicles
• Iteration for computation of the fastest route

Origin Destination Vehicles
0 5 500
2 10 30
7 3 236
8 90 37
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Gawrons Model

• Computation of the departure time
• Through laminar traffic
• Through a preferred speed
• Edges have limited space
• Leaving only if there is a next free edge
• Building of traffic jams

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Dependency between Velocity and Density

• Laminar Traffic
• Capacity dominating
• Congestion area

Source http//www.wikipedia.org
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Extensions

• However,
• O-D Matrices not realistic enough
• O-D Matrices not flexible
• It can be achieved even more efficiency
• Applying of
• Agents
• Event-Driven Queue Based Simulations

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Modelling of Agents

• Replaces O-D Matrixes
• Activities of the single person
• Building of activities through iterations

• Plan 1
• - Home till 9 am
• - Drive to work (car)
• - Work 8h, begin
• approx 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, begin
• approx 8.30 am
• Drive to sports (pt)
• Sports 18 pm to
• 21 pm (optional)
• - Drive home (pt)

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Event-Driven Queue Based Simulations

• Substitution of the constant time-step through
  direct treatment of actions
• Most computational time where traffic flow is
  maximal
• Results
• Simulation performance is being boosted
• Advantageous for the parallel computing
• Fast simulation of huge traffic networks

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Elements of the Event-Driven Queue Based
Simulations
Activity plan
Entry/arrival time
Set timer
Road segment
Clock
Agent
Wake up
Register
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Results from the Event-Driven Queue Based
Simulations

• Independent from the size of the traffic network
• Boosting up with factor of ten in comparison to
  simple Queue model
• There is no case where the other models are faster

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Parallel computing

• Partitioning of the network
• Every partition to a different processor

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

• Test cases Berlin and Brandenburg
• 11,6k nodes and 27,7k edges
• 7,05M simulated persons for 24 hours
• 249M used edges for 24 hours
• Used computer system
• Shared memory parallel computer with 256GB RAM
• 64 dual-core Intel Itanium 2 processors with 1,65
  GHz
• Results
• Boosting up with factor of 53
• Time for simulation 87s

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Efficiency

• Linear factoring to 64 processors
• Best result by 4 processors

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

• Motivation
• Introduction
• Traffic simulation
• Two models
• Nagel-Schreckenberg model
• Cellular automaton
• Essential steps
• Disadvategous
• Queue model
• Queue data structure
• Model of Simao and Powell
• Gawrons model
• Extensions
• Parallel computing
• Results
• Comparison between the two models

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Comparison between the two models

• The Queue model (in general)
• Higher efficiency
• More realism by building of congestions
• Nagel-Schreckenberg model
• A better observation of the interactions between
  the vehicles
• More complex than the Queue model

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• Questions?