Control of Traffic Intensity in Hyperexponential and Mixed Erlang Queueing Systems with a Method Based on SPRT

Abstract

The control of traffic intensity (ρ) is one of the important problems in the study of queueing systems. Rao et al. (1984) developed a method to detect changes in the traffic intensity in queueing systems of the M/G/1 and GI/M/c types based on the Sequential Probability Ratio Test (SPRT). In this paper, SPRT is theoretically investigated for two different phase-type queueing systems which consist of hyperexponential and mixed Erlang. Also, for testing H <inf>0</inf>:ρ=ρ <inf>0</inf> against H<inf>1</inf>:ρ=ρ <inf>1</inf>, Operating Characteristic (OC) and Average Sample Number (ASN) functions are obtained with numerical methods using multipoint derivative equations according to different situations of and β type errors. Afterward, numerical illustrations for each model are provided with Matlab programming. © 2013 Müjgan Zobu and Vedat Saǧlam.