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

Yutaka Sakuma (Corresponding author), Onno Boxma, Tuan Phung-Duc

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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.

Original languageEnglish
Pages (from-to)373-405
Number of pages33
JournalQueueing Systems
Issue number3-4
Publication statusPublished - 1 Aug 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Copyright 2021 Elsevier B.V., All rights reserved.


  • Autoscaling
  • Matrix exponential solution
  • Phase-type demand
  • Workload-dependent service


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