ABOUT PERIODIC STATES OF SYSTEMS OF MASSSERVICE WITH PERIODIC PARAMETERS

Year 2023, Volume: 10 Issue: Prof. Dr. RASKUL IBRAGIMOV Özel Sayısı, 209 - 216, 15.05.2023

Askar Akhmedov

Abstract

In this article periodic solution from the theory of quenes is considered
For the M/M/n/m queue when the Poisson processes are time homogeneous is
given and for arrivals the service time distribution exponential. Arrrivals follow a Poisson distribution with an arrival rate λ (t) that varies with time t
and service times are exponential with a departure rate μ (t). The queue in
discrete points is considered. The distance between discrete points equally
period of λ (t) and μ (t). The queue in discrete points is formed a Markov
chain. This Markov chain aperiodical. This aperiodical Markov chain have
asymptotical stationary solution. If λ (t) and μ (t) continuous density and
λ (t)= λ (t+T) , μ (t) = μ (t+T). The transition probabilities Рij (t) satisfy an
equation of Kolmogorov

Keywords

Poisson distribution, Markov chain, asymptotical stationary solution, probability, exponential distribution.

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