CHARACTERIZATION OF OPTIMAL ORDER OF SERVERS IN A TANDEM QUEUE WITH BLOCKING

Consider a tandem queueing system with m stages with no intermediate storage space between stages j and j + 1, j = 1,..., m-1. There is an unlimited supply of customers in front of the first stage and the output buffer storage for stage m has an unlimited capacity. For this system we consider the problem of allocating m servers, one to each of these m stages such that the customer departure process from the system is stochastically maximized. In this regard we have shown that if the service times of the servers are comparable in the reversed hazard rate (or the usual stochastic) ordering then there exists an optimal allocation where the server allocated to the first stage has a larger mean service time than that assigned to the second stage. These results complement the recent results of Huang and Weiss (1990) and Yamazaki, Sakasegawa and Shanthikumar (1989).