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Dal'nevostochnyi Matematicheskii Zhurnal, 2004, Volume 5, Number 2, Pages 211–217
(Mi dvmg189)
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Non-stationary distribution of customers number in markov queueing systems
N. I. Golovko, V. V. Katrakhov Pacific National University of Economics
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.
Key words:
queueing system theory, input a Poisson stream, exponential service, the infinite and final store, single server, non-stationary distribution of customers number.
Received: 30.12.2004
Citation:
N. I. Golovko, V. V. Katrakhov, “Non-stationary distribution of customers number in markov queueing systems”, Dal'nevost. Mat. Zh., 5:2 (2004), 211–217
Linking options:
https://www.mathnet.ru/eng/dvmg189 https://www.mathnet.ru/eng/dvmg/v5/i2/p211
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