Estimating Traffic Parameters with Rigorous Error Control

To perform a queuing analysis or design in a communications context, we need to estimate the values of the input parameters, specifically the mean of the arrival rate and service time. In this paper, we propose an approach for estimating the arrival rate of Poisson processes and the average service time for servers under the assumption that the service time is exponential. In particular, we derive sample size (i.e., the number of i.i.d. observations) required to obtain an estimate satisfying a pre-specified relative accuracy with a given confidence level. A remarkable feature of this approach is that no a priori information about the parameter is needed. In contrast to conventional methods such as, standard error estimation and confidence interval construction, which only provides post-experimental evaluations of the estimate, this approach allows experimenters to rigorously control the error of estimation.

💡 Research Summary

The paper addresses a fundamental problem in communication‑network analysis: how to estimate the key input parameters—arrival rate λ of a Poisson traffic stream and average service time μ of an exponentially distributed server—while guaranteeing a prescribed relative accuracy ε with confidence 1‑δ before data collection begins. Traditional statistical practice typically relies on post‑experimental standard‑error calculations and confidence‑interval construction, which only tell the analyst after the fact whether the estimate meets the desired precision. Consequently, experimenters often face either insufficient sample sizes (leading to unreliable estimates) or excessive data collection (inflating measurement cost).

The authors propose a pre‑experimental design methodology that derives explicit sample‑size formulas solely from the user‑specified ε and δ, without any prior knowledge of λ or μ. For the Poisson arrival process, they treat the observed counts X₁,…,Xₙ as i.i.d. Poisson(λ) variables. Using Chernoff bounds and a logarithmic transformation, they obtain the tail inequality

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