Comparison of Policies for Routing Customers to Parallel Queueing Systems

Abstract

This paper studies a queueing system with two groups of servers, each with a separate queue, and with arriving customers routed irrevocably to one of the two queues. One natural policy for routing arriving customers is to send them to the queue with the shortest expected delay. Although this shortest delay routing policy (SDR) is known to be optimal if each server group has one server and the service time distribution has nondecreasing failure rate, little is known about the general multiserver case, even with exponential service times. In this paper we show, using a theoretical upper bound, that an optimal policy would produce delays that are almost identical to what would result from combining the two groups. In addition, our simulation results show that SDR performs nearly optimally in every case considered.