A formula for accepting or rejecting customers so as to maximize the expected value of the rewards for service over an infinite planning horizon. By assuming Poisson arrivals and a common exponential service time, the problem can be formulated as an infinite-horizon continuous-time Markov decision problem. A theorem is then presented that considers the fact that the loss from having a server unavailable is usually an increasing function of time if the number of servers is low, and vice versa. More than 500 simulations were run, comparing results with this theorem and with the exponential service-time distribution assumptions for 5 servers and 10 customer classes. The t-test gives preference to the theorem with confidence greater than 0.995.
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