Geodesic
Non-stationary distribution of customers number in markov queueing systems
Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 2, pp. 211-217.

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There are many investigation results devoted to the analysis of the customers distribution in markov non-stationary queueing systems. For the first time non-stationary distribution of customers number in markov non-stationary queueing system $M/M/1$ with constant intensity of input stream $ \lambda $ and service $\mu$ it has been received in Clark's work. However it is impossible to apply a method offered by Clark to the analysis of markov non-stationary queueing systems from wide class, for example, queueing systems $M(t)/M(t)/1$ with variables intensities of input stream $\lambda(t)$ and service $\mu(t)$, or queueing systems with a various configuration, for example, queueing system with the final store and so on. In this work for calculation of customers number probabilities nonstationary distributions in markov non-stationary queueing systems various configuration with variables intensities of input stream $\lambda(t)$ and service $\mu(t)$ the method of making functions is offered with a variation of the right part which is shown on examples of queueing systems $M(t)/M(t)/1$ and $M(t)/M(t)/1/N_{0}$ with infinite and final stores accordingly. 
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N. I. Golovko; V. V. Katrakhov. Non-stationary distribution of customers number in markov queueing systems. Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 2, pp. 211-217. http://geodesic.mathdoc.fr/item/DVMG_2004_5_2_a5/

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