Multiagent Traffic Management: A Reservation-Based Intersection Control Mechanism

1
Multiagent Traffic Management A
Reservation-Based Intersection Control Mechanism

• Roberto Valenti
• Felix Hageloh
• Zhiwei Zhan

2
Overview

• Introduction
• The Model
• The Metric
• Traffic Light Theory
• The Simulator
• Intersection Control Policies
• Coffee break .. ?
• Empirical Results
• Discussion and Conclusion
• Questions

3
Introduction

• Problem for future Traffic Congestion
• Lose productivity
• decrease standard of living in urban settings
• a lot more.

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Introduction

• Current Solutions
• Overpass
• Drawback Expensive, Only worth the cost at the
  most congested intersections
• 2. Traffic lights
• Drawback Inefficient, requiring cars to remain
  stopped even when no cars are present on the
  intersection road.
• Do we have better solution?

5
Introduction

• MASReservation-Based System!
• Every individual car is an independent autonomous
  agent
• There will be mechanisms for coordination among
  independent agents behaviors
• Goal maximize the efficiency of moving cars
  through intersections with minimal centralized
  infrastructure

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The Model of Intersection traffic

• Assumptions of intersection traffic
• Cars can not turn
• All cars begin with the same speed
• Every car is always trying to travel at the speed
  limit
• Every car is capable of reaching the speed limit
  on any roads
• --But how do we measure which
  intersection is better?

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The Metric

• We need metrics
• 1. Safety
• It should be the primary concern
• Considered to be a prerequisite in this paper
• Efficiency
• throughput
• delay

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The Metric

• Throughput
• Its the amount of traffic that can be handled by
  an intersection
• hard to measure precisely
• make qualitative claims regarding throughput of
  three different systems (discussed later)

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The Metric

• Delay--definition
• Its the primary metric considered
• It stands for the effect that the intersection
  has on the overall journey of a vehicle
• What the system want?
• The average delay should be not bad
• The worst delay should be not too bad

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The Metric

• DelayTwo types
• 1. Average Delay
• 2. Maximum Delay
• C set of all vehicles every car in
  C
• t(i) actual arriving time t0(i) optimal
  arriving time

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Traffic Light Theory

• For overpass, the average and maximum delay are
  both zero
• For traffic light, things are more complicated
• the timing of the lights
• how many cars are on the road
• what are the velocities of the other cars

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Traffic Light Theory

• To analyze this model, we need assumptions
• Cars traveling in the same direction do not
  interact with one another
• 2. Cars that have to decelerate due to a red
  light reach the intersection at full speed
  precisely when the light turns green again

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Traffic Light Theory

• The parameters for the formulas
• P the period of the traffic light
• the fraction of the lights period that
  the light spends on green in one direction
• Two constraints
• Pgt0 and 0lt lt1

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Traffic Light Theory

• The delay for one car is dependent only on
• P and
• max delay (1- )P min delay 0
• the average delay is
• the total expected delay is

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Whats next?

• The Simulator
• Intersection Control Policies

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The Simulator
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The Simulator Dimensions

• Simulation values are constant on all the
  experiments
• Number of lanes
• Probabilities of a Vehicle to spawn on each
  direction
• Area of 400X400 m.
• Lanes are 3.5 m wide.
• Vehicles are 2 m wide by 4 m long.

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The Simulator Rules

• Vehicles are randomly spawned with a predefined
  probability.
• Vehicles are placed uniformly at random in one of
  the lanes traveling in that direction.
• Collision?
• Overflow?
• The driver of each vehicle is given the distance
  to the car in front of it.
• Cameras
• Range-Finders

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The Simulator Rules

• Each driver then takes an action based on this
  information
• ACCELERATE (increase velocity by 3 m/s2)
• DECELERATE (decrease velocity by 15 m/s2)
• COAST (maintain current velocity).
• All spawned vehicles are traveling at the speed
  limit.
• Speed Invariant 0 lt speed lt top speed.
• Vehicles position and velocity are updated
  according to the drivers actions.
• Vehicles which have left the domain of the
  simulator are removed from the simulation.
• Each vehicle tracks its own delay.

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The Simulator Driver Agents

• Agents and Simulator are Independent
• Pseudo code
• COAST
• If speed lt speed limit, ACCELERATE
• If less than 1 second or 1 meter behind the
  vehicle in front and speed gt 0, DECELERATE
• If not through the intersection already, interact
  with the intersection as specified separately for
  each Intersection Control Policy.

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Intersection Control Policies

• Three Intersection Control Policies (ICP)
• Overpass
• Traffic Light
• Reservation System

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ICP Overpass

• Is the simplest
• lets vehicles through all the time.
• No explicit third dimension in the simulator
• vehicles traveling in orthogonal directions are
  allowed to travel to pass through one another.
• The overpass is an optimal solution
• Not actually an intersection

Demo
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ICP Traffic light

• Three Parameters
• the period of the light system
• the time between green lights in which all four
  directions lights are red (in fraction)
• the time for which the North/South lights are
  green (in fraction)
• North and South, East and West are always
  identical
• Yellow lights are not necessary

Demo
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ICP Traffic light

• The interaction is sequential
• The driver calculates when it will reach the
  traffic light given its current velocity.
• The driver sends a message to the intersection
  informing it of the time at which the driver
  expects to arrive.
• The intersection responds with the range of times
  during or after the time specified by the driver,
  at which the lights will be green.
• The driver can make any adjustments to ensure
  that the vehicle enters the intersection with
  green lights.

Demo
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ICP Reservation System

• The intersection is divided into an n x n grid of
  reservation tiles, where n is called the
  granularity of the reservation system.
• The reservation system allows the driver agents
  to call ahead and reserve the spaces they will
  need.
• Each tile can be reserved by one car per time
  step.
• To use the reservation system, the car sends a
  message containing several parameters.

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ICP Reservation System

• Parameters
• The time the vehicle will arrive
• The speed at which the vehicle will arrive
• The direction the vehicle will be facing when it
  arrives
• The vehicles maximum velocity
• The vehicles maximum and minimum acceleration
• The vehicles length and width

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ICP Reservation System

• If the driver has not yet made a reservation, it
  sends the intersection a message.
• If the intersection accepts the request, the
  driver agent notes that a reservation has been
  made (parameters are now fixed)
• If the Intersection rejects the request, the
  driver decelerates and tries again at the next
  time step.
• If the driver has made a reservation, it
  determines whether or not it can keep the
  reservation.
• If it determines that it can not meet the
  reservation, it cancels the reservation and the
  reservation-making process begins again.

Demo
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Whats next?

• Coffee break ? (Whats the time?)
• Empirical Results
• Discussion
• Conclusion
• Questions

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Coffee break
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Empirical Results

• Results obtained using the simulator
• The three systems are compared by looking at the
  average and maximum delays

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Results Overpass

• Obviously the most ideal case
• Normally vehicles experience 0 delay
• Delays only occur if vehicles top speed is below
  the speed limit or if traffic is spawned faster
  than it can move through the intersection
• The overpass system gives the lower bound

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Results Traffic Light

• Results are obtained for different periods and
  different spawning probabilities
• In general we can say that for light traffic,
  short periods are better and for heavy traffic,
  long periods
• Traffic light intersections become overloaded
  very quickly

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Results Traffic light

• 1 lane in each direction and a 1 tile reservation
  system

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Results Reservation System

• The graph shows that the reservation system
  performs much better
• Doesnt break down until a much higher traffic
  load
• Before that, the performance is close to the
  overpass system
• On overloading the performance depends on many
  random factors, hence the jagged line

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Results Reservation System - Scalability

• The reservation system outperforms the traffic
  light system, but does it scale when increasing
  the number of lanes?

traffic light period of 20 seconds run for
1,000,000 steps spawning probability 0.001.
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Results Reservation System - Granularity

• Main parameter to set is the granularity of the
  reservation system
• For the first example increasing the granularity
  from 1 to 2 has a big impact

Each data point represents 1,000,000 steps of
simulation
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Results Reservation System - Granularity
Measured for 2 lanes in each direction and a
spawning probability of 0.001.
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Results Reservation System - Granularity

• Apparently odd numbered granularities give worse
  performances
• The problem is deadlocks. They happen when two
  cars traveling in opposite directions compete for
  the same tile
• Hence the granularity should always be at least
  be equal to the number of lanes or a multiple of
  it

Demo
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Results Reservation System - Granularity

• Increasing the granularity increases the
  performance
• However, memory requirements and computational
  cost rise as a square of the granularity

Average delays over at least 500,000 steps.
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Discussion The Real World

• Can this reservation system easily be applied to
  the real world?
• Margin of error is too small for human drivers
• Margin can be increased for human drivers (also
  in mixed scenarios)
• However, for a large number of human drivers the
  system probably performs almost the same as
  traffic lights

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Discussion Related work

• Most other studies on intersection control focus
  on improving current control systems, i.e.
  traffic lights. A similar system was by Kolodko
  and Vlacic and has been successfully implemented
  using autonomous vehicles

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Conclusion

• Two major outcomes of this research
• An intersection simulator with a precise metric
  for measuring intersection control performances
• A new type of intersection control policy that
  outperforms traffic light systems dramatically
• However, many limiting assumptions were made on
  the current research

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Questions

• ?