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

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* <math>n_i(t)</math> =# of jobs in queue ''i'' at time ''t''
* <math>n(t)=(n_1(t), n_2(t), \dots, n_M(t))^T</math>= the system state at time ''t''
* <math>P(k_1, k_2, \dots, k_M, t) = \Pr(n(t)=(k_1, k_2, \dots, k_M)^T)</math>
* <math>P(k_1, k_2, \dots, k_M)=\lim_{t\to\infty}P(k_1,k_2,\dots,k_M,t)</math>
* Arrivals from the outside world are Poisson. All queues have exponential service time distributions.