Jackson's theorem (queueing theory): Difference between revisions

Revision as of 15:22, 16 February 2009

Revision as of 15:23, 16 February 2009

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==Theorem==

In an open [[Jackson network]] of ''m'' queues where the [[utilization]] <math>\rho_i</math> is less than 1 at every queue, the equilibrium state probability distribution exists and for state <math>\scriptstyle{(k_1,k_2,\ldots,k_m)}</math> is given by the product of the individual queue equilibrium distributions

:<math>\pi (k_1,k_2,\ldots,k_m) = \prod_{i=1}^{m} \pi_i(k_i) = \prod_{i=1}^{m} [\rho_i^{k_i} (1-\rho_i)].</math>