Queueing Systems

, Volume 55, Issue 1, pp 9–25 | Cite as

Dynamic routing to heterogeneous collections of unreliable servers

  • K. D. Glazebrook
  • C. Kirkbride


We argue the importance of problems concerning the dynamic routing of tasks for service in environments where the servers have diverse characteristics and are subject to breakdown. We propose a general model in which both service times and repair times at each machine are i.i.d.with some general distribution. Routing decisions take account of queue lengths, machine states (up or down), the elapsed processing times of jobs in service and the times to date of any machine repairs in progress. We develop an approach to machine calibration which yields a machine index which is a function of all of the preceding information. The heuristic which routes all tasks to the machine of current smallest index performs outstandingly well. The approach of the paper is flexible and is capable of yielding strongly performing routing policies for a range of variants of the basic model. These include cases where job processing is lost at each breakdown and where the machine state may be only partially observed.


Dynamic programming Dynamic routing Index policy Lagrangian relaxation Machine breakdowns Policy improvement Semi-Markov decision process 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancasterU.K.
  2. 2.Department of Management ScienceLancaster UniversityLancasterUK

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