Optimal Splitting of Renewal Input Process to a Queueing System and Its Application to a Network

OPTIMAL SPLITTING OF RENEWAL INPUT PROCESS TO A QUEUEING SYSTEM AND ITS APPLICATION TO A NETWORK Masao Mori Tokyo Institute of Technology Hiroshi Shirakawa Tokyo Institute of Technology (Received July 22, 1987; Revised October 30, 1987) Suppose customers over fraction p should be allocated to a single server queueing system by splitting a given input stream. In this paper we fust show that the regular splitting rule, proposed by Hajek [1], minimizes the waiting time of a routed customer in the sense of convex stochastic ordering. However this arrival stream of routed customers is not in general a renewal process, so it is difficult to evaluate characteristics of the waiting time. Then we give upper and lower bounds for the waiting time distribution by using approximated renewal sequences. At last an application of the above evaluating method to a simple network queueing system will be demonstrated.