On a Vacation Queue Approach to Queue Size Computation for a Signalized Traffic Intersection

Abstract

We propose a vacation queue model for a signalized traffic intersection to elucidate intra-cycle queue size variations. Each incoming street to the intersection is modeled to experience Poisson arrivals, and to have finite queue capacity; vehicles arriving to full queue are dropped. Under a fixed-time policy, the queue size dynamics on each street are decoupled. Motivated by vacation queues, an imbedded Markov chain corresponding to queue sizes at the end of cycles is considered, whose transition probabilities are computed from analytical transient solutions of M/D/1/N queues. Sufficient conditions for convergence to steady-state distributions are provided for fixed-time policy. Simulations suggest consistency between the queue sizes computed by the proposed model, and the Webster and time-dependent traffic queue models.