Product Form Solution to Production Systems With Job Type Restricted Machines

In this paper we present a class of queueing models with multiple job types, multiple machines and machine dependent processing times. Each machine is restricted in such a way that it can only handle jobs from a specific, machine dependent, set of job types. If a job arrives at the system and it can be handled by two or more idle machines, then a probability distribution determines to which machine the job is sent. These probability distributions are control parameters for this model and the value of the probabilities influences the performance of the model. Using partial balance equations we show that only for appropriately chosen values of these probabilities, this model has a product form solution. 1 Introduction In research considerable attention has been devoted to product form stationary distributions for queueing models. Most models that are known to have a product form distribution are reversible or quasi reversible ([Muntz, 1972],[Kelly, 1979], [Walrand & Varaiya, 198..