An optimal operating policy is characterized for the infinite-horizon avera
ge-cost case of a single server queueing control problem. The server may be
turned on at arrival epochs or off at departure epochs. Two classes of cus
tomers, each of them arriving according to an independent Poisson processes
, are considered. An arriving 1-customer enters the system if the server is
turned on upon his arrival, or if the server is on and idle. In the former
case, the 1-customer is selected for service ahead of those customers wait
ing in the system; otherwise he leaves the system immediately. 2-Customers
remain in the system until they complete their service requirements. Under
a linear cost structure, this paper shows that a stationary optimal policy
exists such that either (1) leaves the server on at all times, or (2) turns
the server off when the system is empty. In the latter case, we show that
the stationary optimal policy is a threshold strategy, this feature being c
ommonplace in most of priority queueing systems and inventory models. Howev
er, the optimal policy in our model is determined by two thresholds instead
of one. (C) 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 201-
209, 2001.