Two competing queues with linear costs: The ??c-rule is often optimal

A discrete-time model is presented for a system of two queues that compete for the service attention of a single server with infinite buffer capacity. The arrivals are modelled by an i.i.d, random sequence of a general type while the service completions are generated by independent Bernou lli streams, and the allocation of service attention is governed by feedback policies which are based on past decisions and buffer content histories. The cost of operation per unit time is a linear function of the queue sizes. Under the model assumptions, a fixed prioritization scheme, known as the ??c-rule, is shown, to be optimal when the expected long-run average criterion and the expected discounted criterion, over both finite and infinite horizons, are used. The analysis is based on the Dynamic Programming methodology for Markov decision processes and takes advantage of the sample path properties of the adopted state-space model.