Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Product-form solution

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_810

When the steady-state joint probability of the number of customers at each node in a queueing network is the product of the individual probabilities times a multiplicative constant, as in Pr{N1 = n1, N2 = n2,..., NJ = nJ} = Bπ (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 also decompose into separate factors for each node, as it will in open Jackson networks. Variants of these sorts of solutions also occur in some non-network queues, such as those with vacations. Networks of queues; Queueing theory.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA