Delay-minimizing Settings for Fixed-time Traffic Signals at a Single Road Junction

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Abstract
The operation of traffic signals at road junctions is controlled wholly or partly by preset schedules. Expressions for the delay at fixed-time traffic signals have previously been used in several methods of calculating signal settings. These methods give satisfactory results in many cases, but have a number of drawbacks which are largely overcome in a new method described in this paper. This method finds settings that minimize the estimated average delay per unit time to all traffic passing through the road junction, subject to certain constraints imposed by the traffic engineer. It first determines whether there are any settings that both satisfy these constraints and allow all the approaching traffic to pass through the junction in the long run. If there are, it is shown that delay-minimizing settings exist and are essentially unique, and an iterative procedure is given which can be shown to converge to the delay-minimizing settings. A computer program for carrying out the procedure is briefly described, and a few illustrative results are given.

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