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An M/PH/1 queue with workload-dependent processing speed and vacations

Author

Listed:
  • Yutaka Sakuma

    (National Defense Academy of Japan)

  • Onno Boxma

    (Eindhoven University of Technology)

  • Tuan Phung-Duc

    (University of Tsukuba
    VNU Vietnam Japan University)

Abstract

Motivated by the trade-off issue between delay performance and energy consumption in modern computer and communication systems, we consider a single-server queue with phase-type service requirements and with the following two special features: Firstly, the service speed is a piecewise constant function of the workload. Secondly, the server switches off when the system becomes empty, only to be activated again when the workload reaches a certain threshold. For this system, we obtain the steady-state workload distribution and its moments of any order. We use this result to choose the activation threshold such that a certain cost function, involving processing costs, activation costs and mean workload, is minimized.

Suggested Citation

  • Yutaka Sakuma & Onno Boxma & Tuan Phung-Duc, 2021. "An M/PH/1 queue with workload-dependent processing speed and vacations," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 373-405, August.
    • Handle: RePEc:spr:queues:v:98:y:2021:i:3:d:10.1007_s11134-021-09701-2
    DOI: 10.1007/s11134-021-09701-2
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    References listed on IDEAS

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    5. Mohammad Delasay & Armann Ingolfsson & Bora Kolfal, 2016. "Modeling Load and Overwork Effects in Queueing Systems with Adaptive Service Rates," Operations Research, INFORMS, vol. 64(4), pages 867-885, August.
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