informИнформатикаInformatics1816-03012617-6963UIIP NASBinform-225Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕMATHEMATICAL MODELINGСТАЦИОНАРНОЕ РАСПРЕДЕЛЕНИЕ ТАНДЕМНОЙ СИСТЕМЫ МАССОВОГО ОБСЛУЖИВАНИЯ С ДОПОЛНИТЕЛЬНЫМИ ПОТОКАМИ НА СТАНЦИЯХSTATIONARY DISTRIBUTION OF A TANDEM QUEUE WITH ADDITIONAL FLOWS ON THE STATIONS OF THE TANDEMКлименокВ. И.KlimenokV. I.

Минск, пр. Независимости, 4

klimenok@bsu.byБелорусский государственный университетBelarus20170310201703(55)1322Copyright © Клименок В.И., 20172017Клименок В.И.Klimenok V.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://inf.grid.by/jour/article/view/225

Исследуется стационарное поведение тандемной системы, состоящей из конечного числа многолинейных станций без буферов. В систему поступает марковский поток запросов, каждый из которых должен получить обслуживание на всех станциях тандема. Кроме транзитных запросов, на каждую станцию тандема поступает дополнительный марковский поток запросов, которые должны обслужиться на этой и всех последующих станциях тандема. Времена обслуживания запросов на станциях распределены по экспоненциальному закону с параметрами, зависящими от номера станции. Приводятся алгориты для вычисления стационарного распределения тандема и вероятностей потерь, ассоциированных с тандемом.

A tandem queueing system consisting of a finite number of multi-server stations without buffers is analized. The input flow at the first station is a ???????????? (Markovian arrival process). The customers from this flow aim to be served at all stations of the tandem. For any station, besides transit customers proceeding from the previous station, an additional ???????????? flow of new customers arrives at this station directly. Customers from this flow aim to be served at this station and all subsequent stations of the tandem. The service times of customer at the stations are exponentially distributed with the service rate depending of number of the station. The algorithms for culculation of stationary distributions and the loss probabilities associated with the tandem are given.

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The authors declare that there are no conflicts of interest present.