On the output dynamics of production systems subject to blocking

Abstract

Analyzing the output dynamics of a production system gives valuable information for operation and performance evaluation of a production system. In this article, we present an analytical method to determine the autocorrelation of the inter-departure times in queueing networks subject to blocking that can be represented by a Continuous-Time Markov Chain. We particularly focus on production systems that are modeled as open or closed queueing networks, and where stations have phase-type service time distributions. We use the analytical results for the mean and the variance of the time to produce a given number of products in queueing networks to determine the correlation of inter-departure times with different lags. We present a computationally efficient recursive method to determine the correlation of the inter-departure times in open and closed queueing networks. The method also yields closed-form expressions for the correlations of a two-station production line with exponential servers and a finite buffer. We show how the correlations develop with increasing lags subject to different processing time distributions, buffer capacities, and number of stations, in both open and closed queueing networks. As a result, we propose the analytical method given in this study as a tool to study the effects of design and control parameters on the output dynamics of production systems.