Matched queueing system MoPH/G/1

In this paper, we study the matched queueing system, MoPH/G/1, where the type-I input is a Poisson process, the type-II input is a PH renewal process, and the service times are i.i.d. random variables. A necessary and sufficient condition for the stationariness of the system is given. The expectations of the length of the non-idle period and the number of customers served in a non-idle period are obtained.This project is supported by the National Natural Science Foundation of China and partially by the Institute of Mathematics, Academia Sinica.