Asymptotic analysis of MMPP/M/1 retrial queueing system with unreliable server N. M. Voronina, S. V. Rozhkova, E. A. Fedorova
Material type:
ArticleContent type: Текст Media type: электронный Subject(s): системы массового обслуживания | марковский модулированный пуассоновский процесс | асимптотический анализ | очереди повторных попытокGenre/Form: статьи в сборниках Online resources: Click here to access online
In:
Information Technologies and Mathematical Modelling. Queueing Theory and Applications : 20th International Conference, ITMM 2021, named after A. F. Terpugov, Tomsk, Russia, December 1–5, 2021 : revised selected papers P. 356-370Abstract: In this paper, we study a single-server retrial queueing system with arrival Markov Modulated Poisson Process and an exponential law of the service time on an unreliable server. If the server is idle, an arrival customer occupies it for the servicing. When the server is busy, a customer goes into the orbit and waits a random time distributed exponentially. It is assumed that the server is unreliable, so it may fail. The server’s repairing and working times are exponentially distributed. The method of asymptotic analysis is proposed to find the stationary distribution of the number of customers in the orbit. It is shown that the asymptotic probability distribution under the condition of a long delay has the Gaussian form with obtained parameters.
Библиогр.: 20 назв.
In this paper, we study a single-server retrial queueing system with arrival Markov Modulated Poisson Process and an exponential law of the service time on an unreliable server. If the server is idle, an arrival customer occupies it for the servicing. When the server is busy, a customer goes into the orbit and waits a random time distributed exponentially. It is assumed that the server is unreliable, so it may fail. The server’s repairing and working times are exponentially distributed. The method of asymptotic analysis is proposed to find the stationary distribution of the number of customers in the orbit. It is shown that the asymptotic probability distribution under the condition of a long delay has the Gaussian form with obtained parameters.
There are no comments on this title.