informИнформатикаInformatics1816-03012617-6963UIIP NASBinform-83Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕMATHEMATICAL MODELINGСТАЦИОНАРНЫЕ ХАРАКТЕРИСТИКИ НЕНАДЕЖНОЙ СИСТЕМЫ МАССОВОГО ОБСЛУЖИВАНИЯ С ГРУППОВЫМ МАРКОВСКИМ ПОТОКОМ И РЕЗЕРВНЫМ ПРИБОРОМSTATIONARY CHARACTERISTICS OF UNRELIABLE QUEUEING SYSTEM WITH BATCH MARKOVIAN ARRIVAL PROCESS AND RESERVE SERVERКлименокВ. И.KlimenokV. I.klimenok@bsu.byБелорусский государственный университетBelarus201601102016023040Copyright © Клименок В.И., 20162016Клименок 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/83

Исследуется система массового обслуживания с ненадежным прибором и холодным резервированием, состоящая из бесконечного буфера, основного ненадежного прибора и резервного надежного прибора. Термин «холодный резерв» подразумевает, что резервный прибор выключен, пока исправен основной, и включается только при выходе основного прибора из строя. В систему поступает групповой марковский поток запросов. Поломки на основной прибор поступают в марковском потоке. Времена обслуживания на приборах и времена ремонтов распределены по фазовому закону. Выводится условие существования стационарного режима. Приводятся формулы для вычисления основных характеристик производительности системы. Находится преобразование Лапласа – Стилтьеса распределения времени пребывания запроса в системе.

In the paper, a queueing system with unreliable server and so called «cold» redundancy is analyzed. The system consists of an infinite buffer, the main unreliable server and the reliable reserve server. The term «cold reserve» means that the reserve server is off until the main server is in good order and is activated when the main server is under repair. The input flow to the system is a BMAP (Batch Markovian Arrival Process). Breakdowns arrive to the main server according to a MAP (Markovian Arrival Process). Service times as well as repair time have PH (Phase type) distribution. A condition for the stable operation of the system is shown, its stationary distribution and the main characteristics are calculated and the expression for the Laplace – Stieltjes transform of the sojourn time distribution is derrived.

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