Product-form solution

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{N ₁ = n ₁, N ₂ = n ₂,..., N _J = n _J} = Bπ (n ₁)π (n ₂)...π(n _J), 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.