Dynamic routing to heterogeneous collections of unreliable servers
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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.
KeywordsDynamic programming Dynamic routing Index policy Lagrangian relaxation Machine breakdowns Policy improvement Semi-Markov decision process
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- 6.K.R. Krishnan, Joining the right queue: A Markov decision rule. In: Proceedings of the 28th IEEE Conference Decision Control, (1987) 1863–1868.Google Scholar
- 7.S.P. Martin, I. Mitrani, and K.D. Glazebrook, Dynamic routing among several intermittently available servers. In: Proceedings of the 1st EuroNGI Conference on Next Generation Internet Networks, (2005) 1–8.Google Scholar
- 11.M.L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming (Wiley, New York, 1994).Google Scholar
- 12.N. Thomas and I. Mitrani, Routing among different nodes where servers break down without losing jobs. In Proceedings of the IPDS 95, Erlangen (1995).Google Scholar
- 13.H.C. Tijms, Stochastic Models: An algorithmic approach (Wiley, Chichester, 1994).Google Scholar
- 16.P. Whittle, Optimal Control: Basics and beyond (Wiley, New York, 1996).Google Scholar