A Queueing Networks-Based Model for Supply Systems
In this paper, a stochastic approach, based on queueing networks, is analyzed in order to model a supply system, whose nodes are working stations. Unfinished goods and control electrical signals arrive, following Poisson processes, at the nodes. When the working processes at nodes end, according to fixed probabilities, goods can leave the network or move to other nodes as either parts to process or control signals. On the other hand, control signals are activated during a random exponentially distributed time and they act on unfinished parts: precisely, with assigned probabilities, control impulses can move goods between nodes, or destroy them. For the just described queueing network, the stationary state probabilities are found in product form. A numerical algorithm allows to study the steady state probabilities, the mean number of unfinished goods and the stability of the whole network.
KeywordsQueueing networks Supply systems Product–form solution
- 2.Bocharov, P.P., D’Apice, C., Pechinki,n A.V., Salerno, S.: Queueing Theory, Modern Probability and Statistics. VSP, The Netherlands (2004)Google Scholar
- 9.Pasquino, N., Rarità, L.: Automotive processes simulated by an ODE-PDE model. In: Proceedings of EMSS 2012, 24th European Modeling and Simulation Symposium, 19–21 Sept 2012, Vienna, Austria, pp. 352–361 (2012)Google Scholar