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

Yutaka Sakuma; Onno Boxma; Tuan Phung-Duc

doi:10.1007/s11134-021-09701-2

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

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

Stochastic Operations Research

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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.

Original language	English
Pages (from-to)	373-405
Number of pages	33
Journal	Queueing Systems
Volume	98
Issue number	3-4
DOIs	https://doi.org/10.1007/s11134-021-09701-2
Publication status	Published - 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:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

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

UN SDGs

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10.1007/s11134-021-09701-2

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

Abstract

Bibliographical note

Keywords

UN SDGs

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