This paper reports on extensions of previous researches on queues, delays and optimal signal settings at a single intersection controlled by traffic signals. Vehicles are assumed to arrive in a random stream, specified by a Poisson model, but the mean arrival rates are no longer assumed to be constant and are allowed to vary arbitrarily from one time of day to another. Vehicles are assumed to depart at a constant rate during each green period, while there is still a queue. Arrivals at different approaches are assumed to be mutually independent. The intersection is of a general type, specified in the same way as in Allsop's papers. The first part of the paper presents some numerical approximations for mean queue size, maximum queue size and mean delay, for vehicles at a given approach. Simple comprehensive queue and delay formulae are given, expressing mean queue and mean delay as functions of the mean arrival rate at the approach and of the proportion of cycle time that is effectively green for the approach. These results cover the over-saturated case as well as the undersaturated case, so that they can be used for all traffic conditions ranging from light to very heavy. These simple approximations are found to be sufficiently accurate for practical purposes, as a result of comparisons with more accurate approximations and exact calculations. The second part shows how to apply these results to obtain optimal fixed-time signal settings for this general model, using a treatment like allsop's. Firstly, a procedure is found for separating the time period under consideration, typically a whole day, into off-peak periods and peak periods. Then optimal settings are found for the off-peak periods, using Allsop's procedure, and for peak periods, using a new optimisation method in some ways similar to allsop's. The procedure used also takes account of the constraints that are introduced on maximum queue sizes at the approaches. Finally, some possible areas for further research are indicated. /TRRL/

  • Corporate Authors:

    University College London

    Centre for Transport Studies, Gower Street
    London,   United Kingdom  WC1E 6BT
  • Authors:
    • Mayne, A J
  • Publication Date: 1978

Media Info

  • Features: Figures; References;
  • Pagination: 17 p.

Subject/Index Terms

Filing Info

  • Accession Number: 00195021
  • Record Type: Publication
  • Source Agency: Transport Research Laboratory
  • Report/Paper Numbers: Monograph
  • Files: ITRD, TRIS
  • Created Date: Jul 11 1979 12:00AM