Optimal Pricing for an Unbounded Queue

Abstract

The maximization of expected reward is considered for an Mp/M/s queuing system with unlimited queue capacity. The system is controlled by dynamically changing the price charged for the facility's service in order to discourage or encourage the arrival of customers. For the finite queue capacity problem, it has been shown that all optimal policies possess a certain monotonicity property, namely, that the optimal price to advertise is a non-decreasing function of the number of customers in the system. The main result presented here is that for the unlimited capacity problem, there exist optimal stationary policies at least one of which is monotone. Also, an algorithm is presented, with numerical results, which will produce an ε-optimal policy for any ε >; 0, and an optimal policy if a simple condition is satisfied.

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