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Optimization of Cloud Model Based on Shifted N-policy M/M/m/K Queue

Authors:
Zsolt Saffer

Keywords: optimization; cloud model; queueing model; N-policy

Abstract:
In this paper, we present the performance analysis and cost optimization of an Infrastructure-as-a-Service (IaaS) cloud model with a capacity control policy. The Virtual Machines (VM) are modeled as parallel resources, which can be either in active or in standby state. The capacity of the cloud is controlled by changing the number of active VMs. We define a cost model, that the cloud provider encounters. It takes into account both energy consumption and performance measures. The major objective of the work is to provide a tractable analytic model, which is suitable for practical use. For this purpose, we model the cloud services by an $M/M/m/K$ queue. We propose a simple control policy, in which a predefined portion of VMs are always active. The remaining ones are activated simultaneously when the number of requests reaches a threshold and deactivated when the number of requests falls below the predefined portion of active VMs. We call it as shifted $N$-policy. We provide the stationary analysis of the model. We derive closed form results for the distribution of the number of requests and for several performance measures. The cost model leads to a discrete optimization task, which we approximate by a nonlinear continuous optimization task. After applying numerous approximations, we reduce the problem to a nonlinear equation with a specific structure including factorial terms. We provide the approximate solution of the optimization task. The major result of the work is the closed form approximate solution formula, which gives the optimal threshold under the most relevant range of parameters. The formula gives insight into the dependency of the optimum on the model and cost parameters. We provide also illustrating examples for the most important approximations and validate the approximate solution formula by numeric optimization.

Pages: 11 to 20

Copyright: Copyright (c) IARIA, 2021

Publication date: May 30, 2021

Published in: conference

ISSN: 2308-4030

ISBN: 978-1-61208-860-0

Location: Valencia, Spain

Dates: from May 30, 2021 to June 3, 2021