J. Koyanagi et H. Kawai, AN ASSIGNMENT PROBLEM FOR A PARALLEL QUEUING SYSTEM WITH 2 HETEROGENEOUS SERVERS, Mathematical and computer modelling, 22(10-12), 1995, pp. 173-181
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.