Product Form Solution to Production Systems with Job Type Restricted Machines

摘要

In this paper we present a class of queueing models with multiple job types,211u001emultiple machines and machine dependent processing times. Each machine is 211u001erestricted in such a way that it can only handle jobs from a specific, machine 211u001edependent, set of job types. If a job arrives at the system and it can be handled 211u001eby two or more idle machines, then a probability distribution determines to which 211u001emachine the job is sent. These probability distributions are control parameters 211u001efor this model and the value of the probabilities influences the performance of 211u001ethe model. Using partial balance equations we show that only for appropriately 211u001echosen values of these probabilities, this model has a product form solution.