Estimating Traffic Parameters with Rigorous Error Control

Abstract

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.