Stochastic processes and their network representations associated with a production line queuing model

Abstract

The passage of items through the stations of a production line has associated with it different types of random points in time that induce different stochastic point processes. The process of holding times of items at each of k stations is defined; we call it a generalized vector renewal process. The steady-state properties of this process are represented by an activity network. Relationships among random variables of interest are simplified through the use of equivalent networks. Special results are derived for k = 2, k = 3, and k = 4.