THE QNET METHOD FOR REENTRANT QUEUING-NETWORKS WITH PRIORITY DISCIPLINES

This paper is concerned with the estimation of performance measures of two priority disciplines in a d-station re-entrant queueing network. Such networks arise from complex manufacturing systems such as wafer f abrication facilities. The priority disciplines considered are First-B uffer-First-Served (FBFS) and Last-Buffer-First-Served (LBFS). An anal ytical method is developed to estimate the long-run average workload a t each station and the mean sojourn time in the network. When the firs t-buffer-first-served discipline is used, a refined estimate of the me an sojourn time is also developed. The workload estimation has two ste ps. In the first step, following Harrison and Williams (1992), we use a d-dimensional reflecting Brownian motion (RBM) to model the workload process. We prove that the RBM exists and is unique in distribution a nd that it has a unique stationary distribution, We then use an algori thm of Dai and Harrison (1992) to compute the stationary distribution of the RBM. Our method uses both the first and second moment informati on, and it is rooted in heavy traffic theory. It is closely related to the QNET method of Harrison and Nguyen (1993) for two-moment analysis of First-In-First:Out (FIFO) discipline. Our performance estimates of several example problems are compared to the simulation estimates to illustrate the effectiveness of our method.