ABOUT PERIODIC STATES OF SYSTEMS OF MASSSERVICE WITH PERIODIC PARAMETERS

Authors : Askar AKHMEDOV

Pages : 209-216

View : 20 | Download : 34

Publication Date : 2023-05-15

Article Type : Research Paper

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 insert ignore into journalissuearticles values(t); that varies with time t and service times are exponential with a departure rate μ insert ignore into journalissuearticles values(t);. The queue in discrete points is considered. The distance between discrete points equally period of λ insert ignore into journalissuearticles values(t); and μ insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(t); and μ insert ignore into journalissuearticles values(t); continuous density and λ insert ignore into journalissuearticles values(t);= λ insert ignore into journalissuearticles values(t+T); , μ insert ignore into journalissuearticles values(t); = μ insert ignore into journalissuearticles values(t+T);. The transition probabilities Рij insert ignore into journalissuearticles values(t); satisfy an equation of Kolmogorov
Keywords : Poisson distribution, Markov chain, asymptotical stationary solution, probability, exponential distribution