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Optimisation of a generalised M(k)/M/k queueing system

Author

Listed:
  • Tao Yang
  • Wuyi Yue
  • Jianfen Zhan
  • Qiying Hu

Abstract

We study a generalised M(k)/M/k queueing system where the arrival rate depends on the number of servers. There are holding costs reflecting the waiting cost of customers and service costs relating to operation of the servers. The objective is to minimise the total system cost in a steady state. We analyse the cost structure and show that the system holding cost rapidly decreases with the number of servers under some weak conditions. Based on this, we present an upper bound of the optimal number of servers. Finally, numerical examples are given to illustrate the model and the results.

Suggested Citation

  • Tao Yang & Wuyi Yue & Jianfen Zhan & Qiying Hu, 2009. "Optimisation of a generalised M(k)/M/k queueing system," International Journal of Revenue Management, Inderscience Enterprises Ltd, vol. 3(4), pages 428-440.
    • Handle: RePEc:ids:ijrevm:v:3:y:2009:i:4:p:428-440
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    Cited by:

    1. van Sluisveld, Mariësse A.E. & Worrell, Ernst, 2013. "The paradox of packaging optimization – a characterization of packaging source reduction in the Netherlands," Resources, Conservation & Recycling, Elsevier, vol. 73(C), pages 133-142.

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