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Periodic routing to parallel queues and billiard sequences

Author

Listed:
  • Arie Hordijk
  • Dinard van der Laan

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 [InlineMediaObject not available: see fulltext.]−1, where N is the number of different symbols in the sequence which corresponds to the number of parallel queues in the routing problem. Copyright Springer-Verlag 2004

Suggested Citation

  • Arie Hordijk & Dinard van der Laan, 2004. "Periodic routing to parallel queues and billiard sequences," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 173-192, June.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:2:p:173-192
    DOI: 10.1007/s001860300322
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    Cited by:

    1. Bruno Gaujal & Arie Hordijk & Dinard van der Laan, 2005. "On the Optimal Policy for Deterministic and Exponential Polling Systems," Tinbergen Institute Discussion Papers 05-066/4, Tinbergen Institute.
    2. Legros, Benjamin & Jouini, Oualid, 2019. "On the scheduling of operations in a chat contact center," European Journal of Operational Research, Elsevier, vol. 274(1), pages 303-316.

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