AN ANALYTICAL SOLUTION FOR THE DISCRETE-TIME SINGLE-SERVER SYSTEM WITH SEMI-MARKOVIAN ARRIVALS

In this paper we derive an analytical solution for the stationary dist ribution of the number of customers and the idle time in a single serv er system with semi-Markovian arrival processes in discrete time domai n (SM/G/1). This kind of arrival process enables us to take autocorrel ations into account, with various applications for the modeling of com munication and manufacturing systems. It will be shown that the distri bution of the customer number can be represented as a linear combinati on of geometric distributions. Thus a simple calculation of higher mom ents of the customer number is possible.