Generalized confidence interval for R = P(X > Y) of Pareto distribution and its application in Web performance

In this paper we present a method useful for the system engineer to improve the service performance of a Web server through session-based Web workload, the best indicator of the users perception of the Web quality. Bytes transferred per session is one of the characteristics of intra-session which collectively describe session-based Web workload. This characteristic exhibits heavy-tailed behavior and its distribution match well with the Pareto Type I distribution [Goseva-Popstojanova et al. (2006)]. So for the performance study, we estimate the probability, R = P(X >; Y), when X and Y are two independent but not identically distributed random variables following Pareto Type I distribution, using the maximum likelihood estimator. Extensive simulation studies are carried out to study the performance of the estimator. A generalized two-sided confidence interval for R of the Pareto type I distribution is constructed. The derived confidence interval suits both small samples and large samples. The average width and the coverage probability of this confidence interval is compared with the usual asymptotic confidence interval through simulations. Using real data, we illustrate how R and generalized confidence interval of R can be used for improving the service performance of a Web server.