Quasi-reversibility of a discrete-time queue and related models

We consider a discrete-time queueing system and its application to related models. The model is defined byX_n+1=X_n+A_n-D_n+1 with discrete states, whereX_n is the queue-length at the nth time epoch,A_n is the number of arrivals at the start of the nth slot andD_n+1 is the number of outputs at the end of the nth slot. In this model, the arrival process {A_n} is described as a sequence of independently and identically distributed random variables. The departureD_n+1 depends only on the system sizeX_n+A_n at the beginning of the time slot.We study the reversibility for the model. The departure discipline in which the system has quasi-reversibility is determined. Models with special arrival processes were studied by Walrand [8] and sawa [7]. In this paper, we generalize their results. Moreover, we consider discrete-time queueing networks with some reversible nodes. We then obtain the product-form solution for these networks.