Book Chapter10.1007/978-3-030-27181-7_8
A single server queue with workload-dependent service speed and vacations
Yutaka Sakuma,Onno Boxma,Tuan Phung-Duc +2 more
- 27 Aug 2019
- pp 112-127
7
TL;DR: This work considers a queueing system in which the service speed is a function of the workload, and which the server switches off when the system becomes empty, only to be activated again when the workload reaches a certain threshold.
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Abstract: In modern data centers, the trade-off between processing speed and energy consumption is an important issue. Motivated by this, we consider a queueing system in which the service speed is a function of the workload, and in which 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. We use this result to choose the activation threshold such that a certain cost function, involving holding costs and activation costs, is minimized.
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Citations
Queues with workload-dependent arrival and service rates
René Bekker,Sem Borst,Onno Boxma,Offer Kella +3 more
- 01 Jan 2003
TL;DR: In this paper, the authors consider two types of queues with workload-dependent arrival rate and service speed and compare the steady-state distribution of the workload (both at arbitrary epochs and at arrival instants) in two models.
83
Shot-noise queueing models
Onno Boxma,Michel Mandjes +1 more
TL;DR: A survey of so-called shot-noise queues: queueing models with the special feature that the server speed is proportional to the amount of work it faces, and some attention to queues with general workload-dependent service speed.
An M / PH /1 queue with workload-dependent processing speed and vacations.
TL;DR: In this article, 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, and secondly, the server switches off when the system becomes empty, only to be activated again when the workload reaches a certain threshold.
M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis
Mehmet Akif Yazici,Tuan Phung-Duc +1 more
- 31 Aug 2020
TL;DR: In this paper, the authors propose an analytical method for an M/M/1 vacation queue with workload dependent service rates, and obtain the distribution of the workload in the system, and consider a power-saving and performance trade-off problem.
3
Two queues with time-limited polling and workload-dependent service speeds
TL;DR: In this article, the authors study a single-server polling model with two queues, where customers arrive at the queues according to two independent Poisson processes, and the server spends random amounts of time in each queue.
2
References
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Level Crossings in Point Processes Applied to Queues: Single-Server Case
TL;DR: This paper introduces a new methodology for obtaining the stationary waiting time distribution in single-server queues with Poisson arrivals by exploiting the observation that the stationary density of the virtual waiting time can be interpreted as the long-run average rate of downcrossings of a level in a stochastic point process.
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