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Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form

In this paper we present a new method on how to compute the expectation and distribution of the queue length for a particular class of systems. We apply this method and prove its time-efficiency for models in road traffic such as the fixed-cycle traffic light (FCTL) model and for the bulk-service queue model. We give several generalizations of the FCTL queue, which model right-turns, disruptions of the traffic and uncertainty in departure times. We also consider different ways of green time allocation, which are based on either minimizing the maximum expected delay per vehicle or minimizing the total expected queue length. We compare these methods to proportional allocation.