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A Stochastic Breakdown Model for an Unreliable Web Server System and an Optimal Admission Control Policy

Part of: Applications Special processes

Published online by Cambridge University Press:  14 July 2016

Ji Hwan Cha  and
Eui Yong Lee
Ji Hwan Cha*
Affiliation:
Ewha Womans University
Eui Yong Lee*
Affiliation:
Sookmyung Women's University
*
∗Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: [email protected]
∗∗Postal address: Department of Statistics, Sookmyung Women's University, Seoul, 140-742, Korea. Email address: [email protected]
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Abstract

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Web servers have to be protected against overload since overload can lead to a server breakdown, which in turn causes high response times and low throughput. In this paper, a stochastic model for breakdowns of server systems due to overload is proposed and an admission control policy which protects Web servers by controlling the amount and rate of work entering the system is studied. Requests from the clients arrive at the server following a nonhomogeneous Poisson process and each requested job takes a random time to be completed. It is assumed that the breakdown rate of the server depends on the number of jobs which are currently being performed by the server. Based on the proposed model, the reliability function and the breakdown rate function of the server system are derived. Furthermore, the long-run expected number of jobs completed per unit time is derived as the efficiency measure, and the optimal admission control policy which maximizes the efficiency will be discussed.

Keywords

Unreliable serverbreakdown ratereliability functionefficiencyoptimal admission control policy

MSC classification

Secondary: 60K10: Applications (reliability, demand theory, etc.) 62P30: Applications in engineering and industry
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 2 , June 2011 , pp. 453 - 466
Copyright
Copyright © Applied Probability Trust 2011 

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