On Single Server Queues with Batch Arrivals

Авторы: Condratenko A.E., Sobolev V.N.
Журнал: Computer Sciences & Mathematics Forum
Том: 7
Номер: 1
Год издания: 2023
Издательство: MDPI
Местоположение издательства: Basel, Switzerland
Первая страница: 59
Последняя страница: 62
DOI: 10.3390/IOCMA2023-14417
Аннотация: We consider a queuing system 𝐺𝐼𝜈|𝑀|1|∞ with arrival of customers in batches, general renewal arrivals, exponential service times, single service channels and an infinite number of waiting positions, where customers are serviced in the order of their arrival. In the stationary case, new forms of the probability generating functions of the number of clients in the system are derived. These new forms are written in terms of the p.g.f. of the tail distribution function of the number of customers per group and of the p.g.f. of an embedded discrete time homogeneous Markov chain. In a queuing system with a batch Poisson arrival flow 𝑀𝜈𝜆|𝑀𝜇|1|∞, the number of customers in the system can be obtained from the normalized tail distribution.
Добавил в систему: Кондратенко Александр Евгеньевич

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