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  • https://doi.org/10.1093/biomet/49.1-2.163Copy DOI Icon

A theoretical analysis of delays at an uncontrolled intersection

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Abstract

This paper is concerned with the average delay to vehicles on the minor road at a junction where the traffic on the major road has absolute priority. It is assumed that vehicles on the major road arrive at random, and pass through at intervals of not less than a time f1. Vehicles on the minor road arrive at random and pass through at intervals of not less than f2. Further, they cannot enter the junction within a time ax after the previous vehicle on the major road. Thus one minor-road vehicle can pass through a gap of duration between aX and a + /32 in the major-road traffic, two can pass in a gap of between a + fl2 and a + 2/2, and so on. A formula is derived for the average delay to vehicles on the minor road when the system is in statistical equilibrium. Extensive tabulations of this formula have been made, and an extract from these is given. The practical implications of the results are not discussed in the paper, but it is hoped to compare the delays with those obtained with traffic-light control. The problem is similar to those of queueing with priority customers, of the 'service repeat' variety, but there is one important difference: at road junctions of the type considered there is a considerable loss of service time when changing from one type of ' customer' to the other. Typical values of /,J and /12' the two service times, are of the order of 1 or 2 sec., but a gap a of about 7 sec. between two priority 'customers' is required for any non-priority 'customers' to be served. An analysis of a similar problem has been given by Winsten (Beckmann, McGuire & Winsten, 1955), but this was based on more restrictive assumptions. Some special cases of the result obtained here were given by Tanner (1953).

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