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. |

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

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