Journal of the Operational Research Society

, Volume 54, Issue 4, pp 379–389

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

  • P S Ansell
  • K D Glazebrook
  • C Kirkbride
Theoretical Paper

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 

References

  1. Whitt W (1986). Deciding which queue to join: some counter-examples. Opns Res 34: 55–62.CrossRefGoogle Scholar
  2. Liu Z and Righter R (1998). Optimal load balancing on distributed homogeneous unreliable processors. Opns Res 46: 563–573.CrossRefGoogle Scholar
  3. Koole G (1996). On the pathwise optimal Bernoulli routing policy for homogeneous parallel servers. Math Opns Res 21: 469–476.CrossRefGoogle Scholar
  4. Johri PK (1989). Optimality of the shortest line discipline with state dependent service times. Eur J Opl Res 41: 157–161.CrossRefGoogle Scholar
  5. Houck DJ (1987). Comparison of policies for routing customers to parallel queueing systems. Opns Res 35: 306–310.CrossRefGoogle Scholar
  6. Kleinrock L (2002). Creating a mathematical theory of computer networks. Opns Res 50: 125–131.CrossRefGoogle Scholar
  7. Altman E (2000). Applications of Markov decision processes in communication networks: a survey. Rapport de Recherche 3984, INRIA.Google Scholar
  8. Foster I and Kesselman C (eds) (1998). The Grid: Blueprint for a New Computing Infrastructure. Morgan Kaufman: San Francisco.Google Scholar
  9. Braun TD, Siegel HJ, and Maciejewski AA . (2001). Heterogeneous computing: goals, methods and open problems. “PDPTA 2001: Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, (ed. Arabnia HR), pp 1–12. CSREA: Athens”.Google Scholar
  10. Becker KJ, Gaver DP, Glazebrook KD, Jacobs PA and Lawphongpanich S (2000). Allocation of tasks to specialized processors: a planning approach. Eur J Opl Res 126: 80–88.CrossRefGoogle Scholar
  11. Schwartz B (1974). Queueing models with lane selection: a new class of problems. Opns Res 22: 331–339.CrossRefGoogle Scholar
  12. Green L (1985). A queueing system with general-use and limited-use servers. Opns Res 33: 168–182.CrossRefGoogle Scholar
  13. Ross KW and Yao DD (1991). Optimal load balancing and scheduling in a distributed computer system. J Assoc Comput Mach 38: 676–690.CrossRefGoogle Scholar
  14. Dacre MJ, Glazebrook KD and Niño-Mora J (1999). The achievable region approach to the optimal control of stochastic systems (with discussion). J R Stat Soc B 61: 747–791.CrossRefGoogle Scholar
  15. Puterman ML (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley: New York.CrossRefGoogle Scholar
  16. Krishan KR (1987). Joining the right queue: a Markov decision rule. In: Proceedings of the 28th IEEE Conference on Decision and Control, pp 1863–1868.Google Scholar
  17. Tijms HC (1994). Stochastic Models: an Algorithmic Approach. Wiley: Chichester.Google Scholar
  18. Ansell PS, Dacre MJ, Glazebrook KD and Kirkbride C (2000). Optimal load balancing and scheduling in distributed multi-class service systems. Technical Report, Newcastle University.Google Scholar
  19. Hajek B (1985). Extremal splittings of point processes. Math Opns Res 10: 543–556.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan Ltd 2003

Authors and Affiliations

  • P S Ansell
    • 1
  • K D Glazebrook
    • 2
  • C Kirkbride
    • 1
  1. 1.Newcastle University, Newcastle upon TyneUK
  2. 2.University of EdinburghEdinburghUK

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