The Optimality of Connected Policies for Markovian Systems with Two Types of Service

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Abstract
Consider a single station service system with bounded queue capacity and two possible types of service (“fast” and “slow”), operating in discrete time. It is proved that in the search for an optimal policy one need not consider policies hat prescribe one type of service when the system is relatively empty, another type when there are more customers in the system, and the first type again if there are even more customers in the system.

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