A Difference Equation Approach to the Optimal Control of a Multiclass Queue with Discounted Costs.

摘要

This report considers the problem of dynamically selecting one of a finite number of customer classes to serve so that the total expected discounted cost over an infinite horizon is minimized. Decisions are allowed at the time of service completion, or if the server is idle, at the time of customer arrival. It is assumed that customers arrive according to independent Poisson processes with different arrival rates for the various customer classes. Service times are independently distributed and identically distributed for customers of a given class. The cost structure is linear and includes class-dependent holding costs, service costs, and rewards. Difference equations are used to derive a closed form expression for total expected discounted cost given the process begins with an arbitrary number of customers in each customer class in the queue and a non-preemptive priority discipline is used.