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

Revision as of 02:59, 10 December 2005

Revision as of 02:59, 10 December 2005

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* <math>\mu_i</math> = service rate at queue <math>i</math><br>

* <math>\lambda_i</math> = total rate at which jobs arrive at queue <math>j</math><br>

* <math>\forall i,1\leq i\leq M:\rho_i = </math> utilization of the service of at queue <math>i = \frac {\lambda_i}{\mu_i} < 1</math><br>

* <math>n_i(t)</math> =# of jobs in queue i at time t. <br>

* <math>n(t)=(n_1(t), n_2(t), ..., n_M(t))^T</math>= the system state at time t<br>