Minimizing delay at a signalized intersection for time-invariant demand rates

Abstract

A method is described for apportioning the green time of a traffic signal cycle at an intersection among a set of stages (phases) in such a way as to minimize the total or average delay to all the vehicles which use the intersection. It is a variation of the linear programming methods of Allsop and Yagar which maximize capacity for specified upper limits of saturation on the approaches subject to arrival rates being in a specified ratio. By stating the cost functions in a different form it is possible to minimize the total delay, allowing any levels of saturation that are justified in the total system sense. Throughflow equivalents are used for turning movements to allow for lane-sharing by the through and turning vehicles. These flow equivalents can be effectively varied as required from one stage of the traffic signal cycle to another to accommodate variable effects of turning movements on capacity and delay, such as changing the mode of operation for left-turning vehicles from absolute right-of-way to a search for appropriate gaps in priority streams. The solution procedure requires that the cost function at each approach be stated in terms of delay vs effective red time for the known arrival distribution. Approximations are introduced through the use of turning equivalents where certain movements must necessarily share road space and through piecewise-linear approximations to the above delay functions. The arrival distributions are assumed known and stationary. An example of the total method is illustrated for a hypothetical 4-way intersection.