Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T13:16:12.126Z Has data issue: false hasContentIssue false
  • English
  • Français

Equilibrium analysis of a stochastic model of traffic flow

Published online by Cambridge University Press:  24 October 2008

W. J. Gordon  and
G. F. Newell
W. J. Gordon
Affiliation:
Brown University
G. F. Newell
Affiliation:
Brown University
Get access Rights & Permissions [Opens in a new window]

Abstract

A. J. Miller has proposed a stochastic model for the study of highway traffic in one direction along a two-lane road in which the desired speed of a vehicle is sampled from a continuous probability distribution and queues of vehicles are Poisson distributed on the highway. Miller has derived the equilibrium expression for the relation between the spacial densities of all vehicles and the spacial densities of those which are freely travelling. This relationship takes the form of a non-linear integral equation which is left unsolved. The present model differs from the original only in the assumption of a discrete distribution of desired speeds. Although the derivations of the equilibrium equations are based upon different arguments from those of Miller, these relations transform to the corresponding integral equations in the limit of a continuous speed distribution. The main body of the paper is devoted to a detailed investigation of the case of two speeds and asymptotic results are obtained for three speeds.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 2 , April 1964 , pp. 227 - 236
Copyright
Copyright © Cambridge Philosophical Society 1964

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Cox, D. R. and Smith, W. L.Queues (Methuen; London, 1961).Google Scholar
(2)Miller, A. J.Road traffic flow considered as a stochastic process. Proc. Cambridge Philos. Soc. 58 (1962), 312–325;CrossRefGoogle Scholar
corrigendum, Miller, A. J.Road traffic flow considered as a stochastic process. Proc. Cambridge Philos. Soc.. 59 (1963), 508.Google Scholar
(3)Miller, A. J.A queuing model for road traffic flow. J. Roy. Statist. Soc. Ser. B, 23 (1961), 64–75.Google Scholar
(4)Miller, A. J. Road traffic flow treated as a stochastic process. Symposium on the theory of traffic flow; Detroit, 1959 (Elsevier; Amsterdam, 1961).Google Scholar
(5)Takács, L.Introduction to the theory of queues (Oxford University Press; New York, 1962).Google Scholar