A Stochastic Model of Platoon Formation in Traffic Flow

1
A Stochastic Model of Platoon Formation in
Traffic Flow

• USC/Information Sciences Institute
• K. Lerman and A. Galstyan
• USC
• M. Mataric and D. Goldberg
• TASK PI Meeting, Santa Fe, NM
• April 17-19 2001

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Traffic on Automated Highways
Ordinary highway
Platoon formation on an automated highway

• Benefits
• increased safety
• increased highway capacity

3
Our Approach

• Traffic as a MAS
• each car is an agent with its own velocity
• simple passing rules based on agent preference
• distributed mechanism for platoon formation
• MAS is a stochastic system
• stochastic Master Equation describes the dynamics
  of platoons
• study the solutions

4
Traffic as a MAS

• Car agent
• velocity vi drawn from a velocity distribution
  P0(v)
• risk factor Ri agents aversion to passing
• desire for safety (no passing)
• desire to minimize travel time (passing)
• Traffic MAS
• heterogeneous system (velocity distribution)
• on- and off-ramps
• distributed control platoons arise from local
  interactions among cars

5
Passing Rules

• When a fast car (velocity vi) approaches a
  platoon (velocity vc), it
• maintains its speed and passes the platoon with
  probability W
• slows down and joins platoon with probability 1-W
• Passing probability W
• Q(x) is a step function
• R is the same for all agents

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Platoon Formation
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MAS as a Stochastic System

• Behavior of an individual agent in a MAS is very
  complex and has many influences
• external forces may not be anticipated
• noise fluctuations and random events
• other agents with complex trajectories
• probabilistic behavior e.g. passing probability
• While the behavior of each agent is very complex,
  the collective behavior of a MAS is described
  very simply as a stochastic system.

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Physics-Based Models of Traffic Flow

• Gas kinetics models
• similarities between behavior of cars in traffic
  and molecules in dilute gases
• state of the system given by distribution funct
  P(v,x,t)
• Hydrodynamic models
• can be derived from the gas kinetic approach
• computationally more efficient
• reproduce many of the observed traffic phenomena
• free flow, synchronous flow, stop go traffic
• valid at higher traffic densities

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Some Definitions
Density of platoons of size m, velocity v
Initial conditions
where P0(v) is the initial distribution of car
velocities
Car joins platoon at rate
for vgtv
Individual cars enter and leave highway at rate g
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Master Equation for Platoon Formation
Inflow and outflow drive the system into a steady
state
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Average Platoon Size
12
Platoon Size Distribution
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Steady State Car Velocity Distribution
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Conclusion

• Platoons form through simple local interactions
• Stochastic Master Equation describes the time
  evolution of the platoon distribution function
• Study platoon formation mathematically
• But,
• Does not take into account spatial
  inhomogeneities
• Need a more realistic passing mechanism
• effect of the passing lane

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Future work

• Multi-lane model
• for each lane i, Pmi(v,t)
• Passing probability depends on density of cars in
  the other lane, and on platoon size
• Microscopic simulations of the system
• Particle hopping (stochastic cellular automata)
• What are the parameters that optimize
• average travel time
• total flow