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Optimal Routing Policy in Two Deterministic Queues

Bruno Gaujal 1 Emmanuel Hyon 1
1 TRIO - Real time and interoperability
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We consider the problem of routing customers to one of two parallel queues where inter-arrival times and service times are deterministic. We provide an explicit formula for the average waiting time of the customers sent to one of the queues when the routing policy is an upper mechanical word. This formula is based on a special continued fraction decomposition of the service time in the queue. Using this formula we provide an algorithm computing the optimal routing policy for two queues. In general, this policy is an upper mechanical word with a rational ratio, and hence is periodic.
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https://hal.inria.fr/inria-00072648
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Submitted on : Wednesday, May 24, 2006 - 10:29:43 AM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM
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Bruno Gaujal, Emmanuel Hyon. Optimal Routing Policy in Two Deterministic Queues. [Research Report] RR-3997, INRIA. 2000. ⟨inria-00072648⟩

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