Generalised ‘join the shortest queue’ policies for the dynamic routing of jobs to multi-class queues

Abstract

Jobs or customers arrive and require service that may be provided at one of several different stations. The associated routing problems concern how customers may be assigned to stations in an optimal manner. Much of the classical literature concerns a single class of customers seeking service from a collection of homogeneous stations. We argue that many contemporary application areas call for the analysis of routing problems in which many classes of customer seek service provided at a collection of diverse stations. This paper is the first to consider routing policies in such complex environments which take appropriate account of the degree of congestion at each service station. A simple and intuitive class of policies emerges from a policy improvement approach. In a numerical study, the policies were close to optimal in all cases.

Keywords:

• dynamic programming
• heuristics
• multi-class queues
• routing
• scheduling

Acknowledgements

We express our appreciation to a referee, whose comments stimulated a range of improvements to the paper, and to the Engineering and Physical Sciences Research Council for supporting the work of the first and second authors through the award of grant GR/M09308. We thank Professor Isi Mitrani of the Department of Computing Science, Newcastle University, for his invaluable input regarding the modelling of computer systems.