Approximate analysis of a multi-class open queueing network with class blocking and push-out

Abstract

We study a multi-class queueing network which consists of a finite capacity node (node 0) linked to M parallel finite capacity nodes (nodes 1 to M). M classes of customers are assumed. All customers first join node 0. A class i customer after completion of its service at node 0 always joins the ith node. All service times and inter-arrival times are assumed to be exponentially distributed. The service priority at node 0 is head-of-line with preemption. When node i (i=1, 2, ..., M) is full, node 0 cannot process class i customers. In addition to the service priority at node 0, push-out is employed. That is, a customer that arrives at node 0 when the node is full, takes the space of a customer which has the lowest priority among the customers already in the node. If all customers in the node have a higher or equal priority, then the arriving customer is lost. This queueing network is analyzed approximately by decomposing it into individual nodes, and then analyzing each node separately. Node 0 is analyzed using a class by class decomposition. The approximation algorithm has been validated using simulation, and the approximate results have a good error.<>