Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

Authors:
K. D. Glazebrook;R. R. Lumley;P. S. Ansell
Affiliations:
School of Management, Edinburgh University, EH8 9JY, UK;School of Management, Edinburgh University, EH8 9JY, UK;Department of Statistics, University of Newcastle upon Tyne, NE1 7RU, UK
Venue:
Queueing Systems: Theory and Applications
Year:
2003

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Abstract

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.