A queueing model of a production system with two machines, one operator and priorities

Abstract

This paper studies a priority queueing model of a production system in which one operator serves two types of units with overlapping service times. The two types of units arrive in independent Poisson processes. There are two machines in the system. Units of type 1 receive two consecutive types of services at machine #1: the handwork performed by the operator and the automatic machining without the operator. Units of type 2 receive only the handwork performed by the operator at machine #2. The operator attends the two machines according to a strict-priority discipline which always gives units of type 2 higher priority than units of type 1. At each machine the handwork times have a general distribution, and at machine #1 the machining times have an exponential distribution. The Laplace-Stieltjes transform of the queue-size distributions and the waiting time distributions for a stationary process are obtained.