A Sequential Test of Traffic Intensity for the M/M/1 Queueing System

Abstract

This paper deals with testing traffic intensity, which is the most important parameter of the (Formula presented.) queue system. The Wald-type sequential probability ratio test (SPRT) is performed to determine traffic intensity by taking advantage of the fact that the total number of customers arriving up to the kth service period, including the kth service period, has a negative binomial distribution. Acceptance and rejection limits obtained from the SPRT are arranged as a multiple sampling plan. This plan is applied with a finite Markov chain. Then, the Operating Characteristic (OC) function and the Average Sample Number (ASN) are obtained precisely. Obtaining the standard errors of the sample number compared to the studies on SPRT applications is the novelty brought by this paper. The sequential analysis method based on the finite Markov chain is also applied to a numerical sample.