Stationary Distribution of Discrete-Time Finite-Capacity Queue with Re-sequencing

Abstract

The discrete-time re-sequencing model, consisting of one high and one low priority finite-capacity queue and a single server, which serves the low priority queue if and only if the high priority queue is empty, is being considered. Two types of customers, regular and re-sequencing, arrive at the system. The arrival and service processes are geometric, i.e. in each time slot at most one customer of each type may arrive at the system and at most one customer may be served. A regular customer upon arrival occupies one place in the high priority queue. An arriving re-sequencing customer moves one customer from the high priority queue (if it is not empty) to the low priority queue and itself leaves the system. A regular customer which sees the high priority queue full and a re-sequenced customer which sees the low priority queue full, are lost. Using the generating function method the recursive procedure for the computation of the joint stationary distribution of the number of customers in the high and in the low priority queues is derived.