A generalized p-value approach to inference on the performance measures of an M/Ek/1 queueing system

Abstract

The hypothesis tests of performance measures for an M/Ek/1 queueing system are considered. With pivotal models deduced from sufficient statistics for the unknown parameters, a generalized p-value approach to derive tests about parametric functions are proposed. The focus is on derivation of the p-values of hypothesis testing for five popular performance measures of the system in the steady state. Given a sample T, let p(T) be the p values we developed. We derive a closed form expression to show that, for small samples, the probability P(p(T) γ) is approximately equal to γ, for 0 γ 1.