Queue Length in a System with an Autoregressive Hyperexponential Incoming Flow at a Critical Load

Abstract

A study is performed of a single-channel queuing system with two classes of priority requests, a relative priority discipline, a Poisson incoming flow with random intensity, and an infinite number of waiting places. The intensity is selected at the moment the countdown begins until the next request arrives, and the intensity does not change with a predetermined probability. The limit distribution of the number of requests of the lowest priority class at a critical system load is found.