Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T10:01:49.266Z Has data issue: false hasContentIssue false
  • English
  • Français

Delays to road traffic at an intersection

Published online by Cambridge University Press:  14 July 2016

G. F. Yeo  and
B. Weesakul
G. F. Yeo
Affiliation:
Yale University
B. Weesakul
Affiliation:
National Statistical Offices, Bangkok
Get access Rights & Permissions [Opens in a new window]

Abstract

A model for road traffic delays at intersections is considered where vehicles arriving, possibly in bunches, in a Poisson process in a one way minor road yield right of way to traffic, which forms alternate bunches and gaps, in a major road. The gap acceptance times are random variables, and depend on whether or not a minor road vehicle is immediately following another minor road vehicle into the intersection or not.

The transforms of the stationary waiting time and queue size distributions, and the mean stationary delay, for minor road vehicles are obtained by substitution of determined service time distributions into results for a generalisation of the M/G/1 queueing system. Some numerical results are given to illustrate the increase in the mean delay for variable gap acceptance times for a Borel-Tanner distribution of major road traffic, and a partial solution is given for a two way major road.

Type
Research Papers
Information
Journal of Applied Probability , Volume 1 , Issue 2 , December 1964 , pp. 297 - 310
Copyright
Copyright © Applied Probability Trust 

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

Beckmann, M., Mcguire, C. B. and Winsten, C. B. (1956) Studies in the Economics of Transportation. Yale U.P. Google Scholar
Blunden, W. R., Clissold, C. M. and Fisher, R. B. (1962) Distribution of acceptance gaps for crossing and turning manoeuvres. First Biennial Conference of the Australian Road Research Board. Google Scholar
Gaver, D. P. (1962) A waiting line with interrupted service. J. R. Statist. Soc. B 24, 73–90.Google Scholar
Gaver, D. P. (1963) Accomodation of second class traffic. Operat. Res. 11, 73–87.Google Scholar
Miller, A. J. (1961) A queueing model for road traffic flow. J. R. Statist. Soc. B 23, 64–75 Google Scholar
Oliver, R. M. (1961) A traffic counting distribution. Operat. Res. 9, 802–810.Google Scholar
Rice, S. O. (1963) Innage and outage intervals in transmission systems composed of links. Bell System Tech. J. 42, 2267–2283.Google Scholar
Tanner, J. C. (1961) Delays on a two-lane road. J. R. Statist. Soc. B 23, 38–63.Google Scholar
Tanner, J. C. (1962) A theoretical analysis of delays at an uncontrolled intersection. Biometrika 49, 163–170.Google Scholar
Weiss, G. H. and Maradudin, A. A. (1962) Some problems in traffic delay. Operat. Res. 10, 74–104.Google Scholar
Yeo, G. F. (1962) Single server queues with modified service mechanisms. J. Aust. Math. Soc. 2, 499–507.Google Scholar
Yeo, G. F. (1963) Ph.D. thesis, Australian National University.Google Scholar
Bibliography on theory of traffic flow and related subjects (1961) Operat. Res. 9, 568–573.Google Scholar