Sequencing of traffic signals

Optimisation of signal timings at a road junction involves the calculation of both continuous and discrete variables. The continuous ones correspond to times at which signals change whilst the discrete ones correspond to the order, known as the sequence, in which incompatible streams of traffic receive right of way. The optimization can thus be formulated as a bi-level programme with discrete variables at the upper level and continuous ones at the lower. The problem which is addressed in this paper is that of identifying a suitable set of values of the discrete variables to be considered for optimisation of the continuous ones. This is achieved by using an exhaustive technique to generate possible sequences and then identifying classes of these that will give rise to identical performance after optimisation of the continuous variables. In practical examples, the equivalence classes are sufficiently large that a considerable saving in computational effort can be achieved by using a single representative from each class. This bi-level formulation has a computational requirement for the optimisation of fixed-time signal-settings which compares favourably with that of mixed-integer ones. A possible extension of this approach to real-time control is noted.