A stochastic approach for supply systems

This paper focuses on a possible approach for supply systems modeled using queueing networks. According to Poisson processes, unfinished goods and control impulses arrive at the working stations, namely the nodes of the network. When the working process in a node ends, a good moves to another node with fixed probabilities either as a part to process or as a control impulse, or leaves the network. Each control impulse is activated during a random exponentially distributed time. According to some probabilities, activated impulses move an unfinished good from the node they arrive to another node, or destroy another unfinished part. For such a queueing network, a product form solution is found for the stationary state probabilities. The stability of the network, the stationary probabilities and the mean number of unfinished parts are studied via an algorithm. Such results are also useful to analyze a real system for assembling car parts.