Matrix Geometric Analysis of Departure Processes of Queues with Applications to a Pull Serial Line

Abstract

In this paper, we focus on the behavior of a queue in a pull serial line at a throughput process under correlated demands. In order to compute the performance measures of the throughput process, we propose a numeric model and an algorithm which is an extension of the matrix geometric analysis method. By constructing a recursive procedure for calculating the joint distribution of an arbitrary number of consecutive interdeparture times in a PH/G/1/K queue, we obtain explicitly the covariance of nonadjacent interdeparture times, and display the correlation coefficients that reveal the long-range dependence. It confirms some structure properties and produces numerical examples for the lag-n autocorrelation of interdeparture times for several different demand distributions, exhibiting both positive and negative autocorrelation.