A new model of a vehicle-actuated traffic signal is introduced. This model is a natural generalization of the fixed-cycle traffic signal and can be analyzed under certain dependent input conditions. The first model applies to the intersection of 2 one-way, one-lane streets. The time-dependent and asymptotic behaviour of the traffic signal and the traffic queues is determined by using results from the theory of storage. Exact distributions of green times and their moments are determined. Conditions for asymptotic stability are given, and when these conditions are satisfied the steady-state queue sizes are determined. Expected total delay per cycle is used as a criterion of optimality, and the optimal signal settings are given in certain special cases. The model is generalized to include more complicated intersections, such as the intersection of k=2 one-way, one-lane streets, a four-way intersection with no left-turning vehicles, and a four-way intersection with a separate cycle phase for left-turning vehicles. Two types of dependent input processes are considered-Markov chains and martingales. Many of the preceding results carry over to these types of input processes. /author/
Abstract