Monotonic and insensitive optimal policies for the control of queues with undiscounted costs

S. Stidham, Jr and R.R. Weber, Operations Research 37 611-625, 1989.

Abstract

We consider the problem of controlling the service and/or arrival rate in 
queues, with the objective of minimizing the total expected cost to reach state 
zero.  We present a unified, simple method for proving that an optimal policy is 
monotonic in the number of customers in the system.  Applications to 
average-cost minimization over an infinite horizon are given.  Both exponential 
and non-exponential models are considered; the essential characteristic is a 
left-skip-free transition structure and a nondecreasing (not necessarily convex) 
holding-cost function.  Some of our results are insensitive to service-time 
distributions.

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