Relations in the Central Limit Theorem Version of the Response Time Law

Abstract

We study the accuracy of the estimators of mean response time and throughput in closed interactive systems such as Web systems. The response time law allows us to calculate the throughput from the mean response time and vice versa. However, we find that the accuracy of the two estimators can be quite different. We refine the response time law using the central limit theorem and study the asymptotic accuracy of the estimators when the measurement time approaches infinity. Based on the asymptotic accuracy of the estimators, we derive rules of thumb for the accuracy of the measured mean response time and measured throughput. Extensive simulation study suggests that the rules of thumb are often valid under realistic measurement time.