Far Eastern Mathematical Journal

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Non-stationary distribution of customers number in markov queueing systems


N. I. Golovko, V. V. Katrakhov

2004, issue 2, Ñ. 211–217


Abstract
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.

Keywords:
queueing system theory, input a Poisson stream, exponential service, the infinite and final store, single server, non-stationary distribution of customers number

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References

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