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

Revision as of 02:48, 10 December 2005

Revision as of 02:51, 10 December 2005

Line 5:

* <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 at queue <math>i = 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>

* <math>P(k_1, k_2, ..., k_M, t)=Pr(n(t)=k_1, k_2, ..., k_M)^T)</math><br>

* <math>P(k_1, k_2, ..., k_M)=\lim_{t\to\infty}P(k_1,k_2,...,k_M,t)</math><br>

* Arrivals from the outside world are Poisson. All queues have exponential service time distributions. <br>

<br>