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Authors: | Ulrich Fiedler |
Group: | Communication Systems |
Type: | Techreport |
Title: | Using Quantiles to Characterize User-Perceived Latency in Simulations with Heavy-Tailed Input |
Year: | 2003 |
Month: | January |
Pub-Key: | UFTransient03 |
Rep Nbr: | 158 |
Abstract: | Simulations with web workloads, which use input generated by sampling a heavy-tailed object size distribution, remain in transient state over all periods of time. This means that all statistics that depend on moments of such a heavy-tailed object size distribution, as e.g. the average object size or the average user-perceived latency of downloads, do not converge within any reasonable time. We therefore investigate whether quantiles of user-perceived latencies are suitable statistics for the performance evaluation in such simulations. We exploit the fact that quantiles of a heavy-tailed distribution do not depend on the moments of the distribution. We show that quantiles in samples from a heavy-tailed distribution converge to a normal distribution in reasonable periods of time. Hence, if latency is approximately proportional to the object size, latency quantiles in simulation output also converge to a normal distribution. Therefore we propose a method to reliably test for this convergence. We validate this method by a simulation study which shows convergence if the network utilization is not too high. Our work suggests that latency quantiles are indeed promising statistics to evaluate simulations with web traffic. |
Resources: | [BibTeX] |