Dynamic Scheduling of a Multiclass Queue: Discount Optimality

J. Michael Harrison

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Advanced Queuing Theory Analysis Scheduling and Optimization Algorithms Optimization and Search Problems

Abstract

We consider a single-server queuing system with several classes of customers who arrive according to independent Poisson processes. The service time distributions are arbitrary, and we assume a linear cost structure. The problem is to decide, at the completion of each service and given the state of the system, which class (if any) to admit next into service. The objective is to maximize the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon, the interest rate being positive. One very special type of scheduling rule, called a modified static policy, simply enforces a (nonpreemptive) priority ranking except that certain classes are never served. It is shown that there is a modified static policy that is optimal, and a simple algorithm for its computation is presented.

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References

1970Principles of Operations Research.1971Characterization and Computation of Optimal Policies for Operating an M/G/1 Queuing System with Removable Server

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1991Due-Date Setting and Priority Sequencing in a Multiclass M/G/1 Queue 1980Dynamic Decisions and Work Load in Multitask Supervisory Control 2014Four proofs of Gittins’ multiarmed bandit theorem 1977Human-Computer Interaction in Multitask Situations 1993Dynamic Scheduling of a Multiclass Fluid Network 2003Whittle's index policy for a multi-class queueing system with convex holding costs 1987On the Optimal Control of Two Queues with Server Setup Times and Its Analysis 1985K competing queues with geometric service requirements and linear costs: The μc-rule is always optimal

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