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Multi-layered round robin routing for parallel servers

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Abstract

We study a system of several identical servers in parallel, where a routing decision must be made immediately on a job’s arrival. Jobs arrive according to a Poisson process, with their processing times following a discrete distribution with finite support. The processing time of a job is known on arrival and may be used in the routing decision. We propose a policy consisting of multi-layered round robin routing followed by shortest remaining processing time scheduling at the servers. This policy is shown to have a heavy traffic limit that is identical to one in which there is a single queue (no routing) and optimal heavy traffic scheduling. In light traffic, we show that the performance of this policy is worse than round robin routing followed by shortest remaining processing time scheduling. We also quantify the difference between round robin and multi-layered round robin routing, which in turn yields insights on the relative importance of routing versus (local) scheduling in such systems.

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Authors and Affiliations

  1. Department of Computing and Software, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canada

    Douglas G. Down & Rong Wu

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  1. Douglas G. Down
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  2. Rong Wu
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Correspondence to Douglas G. Down.

Additional information

AMS subject classifications: 68M20 · 60K25

(Work done while both authors were visitors at EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.)

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Down, D.G., Wu, R. Multi-layered round robin routing for parallel servers. Queueing Syst 53, 177–188 (2006). https://doi.org/10.1007/s11134-006-7419-9

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  • DOI: https://doi.org/10.1007/s11134-006-7419-9

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