Product-form solution

In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of components can be written as a product of the metric across the different components. Using capital Pi notation a product-form solution has algebraic form

${\displaystyle {\text{P}}(x_{1},x_{2},x_{3},\ldots ,x_{n})=B\prod _{i=1}^{n}{\text{P}}(x_{i})}$

where B is some constant. Solutions of this form are of interest as they are computationally inexpensive to evaluate for large values of n. Such solutions in queueing networks are important for finding performance metrics in models of multiprogrammed and time-shared computer systems.