On Estimates of Average Queue Length for Queueing Systems in The Case of Correlated Input Flow

A mathematical model of the simplest single-channel queueing system (QS) in the case of an input flow with certain correlation is considered. Various extensions of the Pollaczek - Khinchin formula of the average queue length are obtained for this QS. A time interval model of the input flow is proposed, within which an expression of the average queue length by unconditional second moments is obtained. All results were obtained under highly general assumptions of ergodicity and stationarity. The results of numerical experiments confirming the theoretical conclusions are cited.