Multistage flow line analysis with the stopped arrival queue model

Abstract

In a stopped arrival queue the arrival process is switched off as soon as the available queue space is full and not switched on again until there is space in the queue. A simple approximation for GI/GI/1/N stopped arrival queues is developed and shown to be remarkably accurate in predicting throughput. Becausea two-stageflowline is equivalent to a stopped arrival queue, the GI/GI/1/N stopped arrival queue can be usedas the building block for approximating the performance of multistage flowlineswhere the service times at the stages have general distributions. Numerical tests of the throughput approximation show that it gives accurate throughput predictions, in spite of its simplicity and minimal computation requirements.

Notes

John Buzacott is a Professor in the Faculty of Administrative Studies at York University. His research interests are in modelling manufacturing systems and in manufacturing and operations strategy. He holds a B.E. degree in Electrical Engineering from the University of Sydney, Austraha, and M.Sc. and Ph.D. from the University of Birmingham, England. He was Chair of the ORSA Technical Section on Manufacturing and Operations Management for 1993–4.

Xiao-Gao Liu received the Ph.D. degree in Management Sciences from the University of Waterloo in 1990. His main research interest is in the area of stochastic models and their application to manufacturing system design, equipment maintenance, and product planning and development. He has recently joined the Systems Engineering Division of Bell-Northern Research.

J. George Shanthikumar received the B.Sc. degree in mechanical engineering from the University of Sri Lanka, Peradeniya, and the M.A.Sc. and Ph.D. degrees in industrial engineering from the University of Toronto, Canada. He is Professor of Industrial Engineering and Operations Research (in the College of Engineering) and Management Science (in the Walter A. Haas School of Business) at the Uni~ersity of California, Berkeley. His research interests are in production systems modelling and analysis, queueing theory, reliability, scheduling, stochastic processes and simulation. He has written or written jointly over 200 technical papers on these topics. He is a coauthor (with John A. Buzacott) of the book Stochastic Models of Manufacturing Systems and a coauthor (with Moshe Shaked) of the book Stochastic Orders and Their Applications.