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

2. Traffic on Automated Highways Ordinary highway • Benefits • increased safety • increased highway capacity Platoon formation on an automated highway

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 factorRi : agent’s 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

6. v1 vC vC v2 v2 vC vC Platoon Formation

7. 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.

8. 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

9. 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 v>v’ Individual cars enter and leave highway at rate g

10. loss due to collisions merging of smaller platoons inflow of cars outflow of cars Master Equation for Platoon Formation Inflow and outflow drive the system into a steady state

11. Average Platoon Size

12. Platoon Size Distribution

13. Steady State Car Velocity Distribution

14. 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

15. 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