The Initial Busy Cycle of a Discrete-Time GI/G/1 Queue in which the Inter-Arrival Times are not Necessarily Identically Distributed

摘要

This paper studies a generalization of the discrete-time GI/G/1 queueing system. Here, the inter-arrival times are not necessarily identically distributed. A recursive scheme is derived to obtain the joint distribution of the duration of the initial busy period, the duration of the first idle period and the number of customers served during the initial busy period. (Author)