Kinetic Theory of Traffic Flows

E. Ben-Naim and P. L. Krapivsky
Additional contact information
E. Ben-Naim: Los Alamos National Laboratory, Theoretical Division and Center for Nonlinear Studies
P. L. Krapivsky: Boston University, Center for Polymer Studies and Department of Physics

A chapter in Traffic and Granular Flow’01, 2003, pp 155-168 from Springer

Abstract: Abstract We describe traffic flows in one lane roadways using a kinetic theory, with special emphasis on the role of quenched randomness in the velocity distributions. When passing is forbidden, growing clusters are formed behind slow cars and the cluster velocity distribution is governed by an exact Boltzmann equation which is linear and has an infinite memory. The distributions of the cluster size and the cluster velocity exhibit scaling behaviors, with exponents dominated solely by extremal characteristics of the intrinsic velocity distribution. When passing is allowed, the system approaches a steady state, whose nature is determined by a single dimensionless number, the ratio of the passing time to the collision time, the two time scales in the problem. The flow exhibits two regimes, a laminar flow regime, and a congested regime where large slow clusters dominate the flow. A phase transition separates these two regimes when only the next-to-leading car can pass.

Keywords: Velocity Distribution; Collision Rate; Traffic Flow; Kinetic Theory; Maxwell Model (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-10583-2_15

Ordering information: This item can be ordered from
http://www.springer.com/9783662105832

DOI: 10.1007/978-3-662-10583-2_15

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().