AN ASSIGNMENT PROBLEM FOR A PARALLEL QUEUING SYSTEM WITH 2 HETEROGENEOUS SERVERS

In this paper, we consider an optimization problem for a parallel queu eing system with two heterogeneous servers. Each server has its own qu eue and customers arrive at each queue according to independent Poisso n processes. Each service time is independent and exponentially distri buted. When a customer arrives at queue 1, the customers in queue 1 ca n be transferred to queue 2 by paying an assignment cost which is prop ortional to the number of moved customers. Holding cost is a function of the pair of queue lengths of the two servers. Our objective is to m inimize the expected total discounted cost. We use the dynamic program ming approach for this problem. Considering the pair of queue lengths as a state space, we show that the optimal policy has a switch over st ructure under some conditions on the holding cost.