Dynamic routing to heterogeneous collections of unreliable servers |
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Authors: | K D Glazebrook C Kirkbride |
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Institution: | (1) Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.;(2) Department of Management Science, Lancaster University, Lancaster, LA1 4YX, UK |
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Abstract: | 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.
AMS Subject Classifications 49L20, 90B22 |
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Keywords: | Dynamic programming Dynamic routing Index policy Lagrangian relaxation Machine breakdowns Policy improvement Semi-Markov decision process |
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