M/D/1 queue: Difference between revisions

Revision as of 17:00, 7 November 2018

Revision as of 04:28, 5 February 2019

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=== Transition Matrix ===

The transition probability matrix for aan M/D/1 queue with arrival rate λ and service time 1, such that λ <1 (for stability of the queue) is given by P as below:<ref name=":1" />

<math>P=\begin{pmatrix} a_0 & a_1 & a_2 & a_3 & ... \\ a_0 & a_1 & a_2 & a_3 & ...\\ 0 & a_0 & a_1 & a_2 & ...\\ 0&0 & a_0 & a_1 & ...\\... & ... &...&... &...\\\end{pmatrix}</math> ， <math>a_n=\frac{\lambda^n}{n!}e^{-\lambda}</math>, n = 0,1,....