Mark E. Lewis
Cornell
University
School of Operations Research and Information
Engineering
226 Rhodes Hall
Ithaca, New York
14853
Douglas G. Down
Department of
Computing and Software
McMaster University
1280 Main
Street West
Hamilton, ON L8S 4L7, Canada
In this paper we introduce a new method of mitigating the problem of long wait times for low
priority customers in a two-class queueing system. To this end, we allow class 1 customers to
be “upgraded” to class 2 after they have been in queue for some time. We assume there are
ci servers at station i, i = 1, 2. The servers at station 1 are flexible in the sense that they can
work at either station while the servers at station 2 are dedicated. Holding costs at rate hi are
accrued per customer per unit time at station i, i = 1, 2. This study yields several surprising
results. First, we show that stability analysis requires a condition on the order of the service
rates. This is unexpected since no such condition is required when the system does not have
upgrades. This condition continues to play a role when control is considered. We provide
structural results which include a c − μ rule when an inequality holds and a threshold policy
when the inequality is reversed. A numerical study verifies that the optimal control policy
significantly reduces holding costs over the policy that assigns the flexible server to station
1. At the same time, in most cases the optimal control policy reduces waiting times of both
customer classes.