Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Product-Form Solution

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1153-7_200649

When the steady-state joint probability of the number of customers at each node (station) in a queueing network is the product of the individual probabilities times a multiplicative constant, as in Pr{N1 = n1, N2 = n2,…, NJ = nJ} = Kπ(n1)π(n2)…π(nJ), the network is said to have a product-form solution. Sometimes the designation of a product-form solution requires that the multiplicative constant K also decompose into separate factors for each node, as holds for open Jackson networks but not for closed Jackson networks. Variants of such product-form solutions also occur in some non-network queues, such as those with vacations.

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© Springer Science+Business Media New York 2013