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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: jhcha@ewha.ac.kr
∗∗Postal address: Department of Statistics, Sookmyung Women's University, Seoul, 140-742, Korea. Email address: eylee@sookmyung.ac.kr
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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 

References

Agustin, M. A. (2003). Statistical properties of a system reliability estimator using the Littlewoood software reliability model. J. Appl. Prob. 40, 766–778.Google Scholar
Agustin, M. A. and Peña, E. A. (1999). A dynamic competing risks model. Prob. Eng. Inf. Sci. 13, 333–358.CrossRefGoogle Scholar
Barghout, M. (2010). Predicting software reliability using an imperfect debugging Jelinski Moranda non-homogeneous Poisson process model. Model Assisted Statist. Appl. 5, 31–41.Google Scholar
Bhatti, N. and Friedrich, R. (1999). Web server support for tiered services. IEEE Network 13, 64–71.Google Scholar
Boland, P. J. and Ni Chuı´v, N. (2007). Optimal times for software release when repair is imperfect. Statist. Prob. Lett. 77, 1176–1184.Google Scholar
Boland, P. J. and Singh, H. (2002). Determining the optimal release time for software in the geometric Poisson reliability model. Internat. J. Reliab. Quality Safety Eng. 9, 201–213.CrossRefGoogle Scholar
Boland, P. J., Singh, H. and Cukic, B. (2002). Stochastic orders in partition and random testing of software. J. Appl. Prob. 39, 555–565.CrossRefGoogle Scholar
Casella, G. and Berger, R. L. (2002). Statistical Inference, 2nd edn. Duxbury, CA.Google Scholar
Jelinski, Z. and Moranda, P. (1972). Software reliability research. In Statistical Computer Performance Evaluation, ed. Freiberger, W., Academic Press, New York, pp. 465–484.CrossRefGoogle Scholar
Kvam, P. H. and Peña, E. A. (2005). Estimating load-sharing properties in a dynamic reliability system. J. Amer. Statist. Assoc. 100, 262–272.Google Scholar
Ling, Y. and Mi, J. (2004). An optimal trade-off between content freshness and refresh cost. J. Appl. Prob. 41, 721–734.Google Scholar
Mi, J. (2002). Age-replacement policy and optimal work size. J. Appl. Prob. 39, 296–311.Google Scholar
Ross, S. M. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
Singpurwalla, N. D. (1991). Determining an optimal time interval for testing and debugging software. IEEE Trans Software Eng. 17, 313–319.Google Scholar
Voigt, T. and Gunningberg, P. (2001). Kernel-based control of persistent web server connections. In ACM SIGMETRICS Performance Evaluation Review, Association for Computing Machinery, New York, pp. 20–25.Google Scholar
Voigt, T., Tewari, R., Freimuth, D. and Mehra, A. (2001). Kernel mechanisms for service differentiation in overloaded web servers. In Proc. General Track: 2002 USENIX Ann. Tech. Conf., ed. Park, Y., pp. 189–202.Google Scholar
Wessels, D. (2001). Web Caching. O'Reilly, Sebastopol, CA.Google Scholar