The Streetwalker’s Dilemma: A Job Shop Model

Abstract

We consider the problem of maximizing the long-run average return in a single server traffic reward system in which the customer’s offer, a joint distribution of reward and of service time required to earn this reward, is independent of the renewal process which governs customer arrivals. After formulating the problem as a semi-Markov decision process, we characterize the form of an optimal policy. When the renewal process is Poisson, the characterization is easily stated : accept a customer if and only if the ratio of his expected reward to his expected service time is larger than g, the long-run average return. When the arrival process is Poisson, g is easily found. Next, batch arrivals are permitted, and further results are obtained.

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