Dynamic Admission and Service Rate Control of a Queue
K. M. Adusumilli and J. J. Hasenbein
This paper investigates a queueing system in which the controller can
perform admission and service rate control. In particular, we examine
a single server queueing system with Poisson arrivals and exponentially
distributed services with adjustable rates. At each decision epoch the
controller
may adjust the service rate. Also, the controller can reject incoming
customers
as they arrive. The objective is to minimize long-run average costs
which
include: a holding cost, which is a non-decreasing function
of the number of jobs in the system; a service rate cost c(x),
representing
the cost per unit time for servicing jobs at rate x; and a rejection
cost
K for rejecting a single job. From basic principles, we derive
a simple, efficient algorithm for computing the optimal policy. Our
algorithm
also provides an easily computable bound on the optimality gap at every
step.
The algorithm presupposes that stationary policies are optimal for this
problem,
a result that we also establish in the last section of the paper.