Control of traffic intensity in hyperexponential and mixed Erlang queueing systems with a method based on SPRT (Q459663)

Summary: The control of traffic intensity \((\rho)\) is one of the important problems in the study of queueing systems. \textit{S. S. Rao} et al. [Opsearch 21, 63--80 (1984; Zbl 0546.60096)] 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 \(H_0:\rho=\rho_0\) against \(H_1:\rho=\rho_1\), Operating Characteristic (OC) and Average Sample Number (ASN) functions are obtained with numerical methods using multipoint derivative equations according to different situations of \(\alpha\) and \(\beta\) type errors. Afterward, numerical illustrations for each model are provided with Matlab programming.