A New Technique in the Optimization of Exponential Queueing Systems

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Abstract
The problem of controlling M/M/c queueing systems with c = or 1 is considered. By providing a new definition of the time of transition, we enlarge the standard set of decision epochs, and obtain a preferred version of the n- period problem in which the times between transitions are exponential random variables with constant parameter. Using this new technique, we are able to use the inductive approach in a manner characteristic of inventory theory. The efficacy of the approach is then demonstrated by successfully finding the form of an optimal policy for four quite distinct models that have appeared in the literature; namely, those of (i) McGill, (ii) Miller-Cramer, (iii) Crabill-Sabeti, and (iv) Low. Of particular note, one analysis establishes that an (s, S) or control-limit policy is optimal for an M/M/c queue with switching costs and removable servers.

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