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Updated: Nov 11, 2025

A Quantitative Fitness Analysis Workflow
Published on: August 13, 2012
An M/PH/1 queue with workload-dependent processing speed and vacations
Yutaka Sakuma1, Onno Boxma2, Tuan Phung-Duc3,4
1Department of Computer Science, National Defense Academy of Japan, Yokosuka, Japan.
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.
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