| 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. |
