The Policy Space Structure of Markovian Systems with Two Types of Service

A system with customers demanding service is observed at equally spaced points in time. Two types of service can be applied and the maximum number of customers the system can accommodate is L. The probability for an arrival of a customer per period is assumed to be \lambda, and the probability to finish its service in one period will be \mu _k (k - 1, 2). Different costs are imposed on the system for using a certain type of service as well as for a customer lost. The implementation of a particular service policy generates a Markov process. The policy space structure and its relationship to the variants of the system (costs, probability to finish service in a unit of time, and arrivals) is presented. The analysis shows that it is possible to reduce the number of policies to be considered from 2^L+1 to L + 2, and a simple algorithm is proposed for choosing the optimal policy.