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Periodic routing to parallel queues and billiard sequences

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Abstract.

In this companion paper of [10] we introduce the combinatorial notion of unbalance for a routing pattern. Using this unbalance we derive an upper bound for the total average expected waiting time of jobs which are routed to parallel queues according to a periodic routing rule. A billiard sequence is obtained with unbalance smaller than or equal to −1, where N is the number of different symbols in the sequence which corresponds to the number of parallel queues in the routing problem.

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Authors and Affiliations

  1. Mathematical Institute, Leiden University, P.O. Box 9512, 2300RA, Leiden, The Netherlands

    Arie Hordijk

  2. Mathematical Institute, Leiden University, P.O. Box 9512, 2300RA, Leiden, The Netherlands

    Dinard van der Laan

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  1. Arie Hordijk
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  2. Dinard van der Laan
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Correspondence to Arie Hordijk.

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Hordijk, A., van der Laan, D. Periodic routing to parallel queues and billiard sequences. Math Meth Oper Res 59, 173–192 (2004). https://doi.org/10.1007/s001860300322

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  • DOI: https://doi.org/10.1007/s001860300322

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