Abstract
ABSTRACT We consider an admission control model of a discrete-time queueing system, in which the optimal policy was known to be of threshold type [2,5]. A threshold policy is characterized by two parameters (L,η) in that an arriving customer is admitted (resp. rejected) if the queue size is below (resp. above) the integer threshold L, and if the queue size is exactly L, then the customer is admitted (resp. rejected) with probability η (resp. 1-η). In this paper, we consider the adaptive version of the problem in which the parameters L and η are not available, this being the case if, e.g., the actual values of the model parameters, the arrival and service rates, are not known. We propose to implement the optimal threshold policy via an adaptive policy in terms of an adaptive algorithm of the stochastic approximation type. The proposed algorithm is simple, and easy to implement on-line. Convergence of the algorithm and the optimality of the adaptive policy are shown.
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