informИнформатикаInformatics1816-03012617-6963UIIP NASBinform-6Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕMATHEMATICAL MODELINGМНОГОКАНАЛЬНАЯ СИСТЕМА ОБСЛУЖИВАНИЯ С МАРКОВСКИМ ВХОДНЫМ ПОТОКОМ НЕТЕРПЕЛИВЫХ ЗАПРОСОВ, ФУНКЦИОНИРУЮЩАЯ В СЛУЧАЙНОЙ СРЕДЕMULTISERVER QUEUEING SYSTEM WITH MARKOVIAN ARRIVAL FLOW OF IMPATIENT CUSTOMERS OPERATING IN A RANDOM ENVIRONMENTДудинС. А.DudinS. A.dudin85@mail.ruДудинаО. С.DudinaO. S.dudina_olga@email.comБелорусский государственный университетBelarus201525092016014555Copyright © Дудин С.А., Дудина О.С., 20162016Дудин С.А., Дудина О.С.Dudin S.A., Dudina O.S.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/6

Исследуется многолинейная система массового обслуживания с бесконечным буфером и нетерпеливыми запросами, функционирующая в случайной среде. В систему поступает марковский входной поток запросов. Время обслуживания запроса имеет распределение фазового типа. В течение времени ожидания в буфере запросы могут проявлять нетерпеливость и покидать систему без обслуживания. Параметры системы зависят от состояния случайной среды. Находится условие существования стационарного режима. Приводятся формулы для вычисления основных характеристик производительности системы. Находится преобразование Лапласа – Стилтьеса распределения времен ожидания и пребывания запроса в системе.

Multiserver queuing system with an infinite buffer and impatient customers, operating in a random environment is investigated. Customers arrive to the system according to the Markovian arrival flow. Service time of a customer has a phase type distribution. During the waiting time in the buffer customers can be impatient and leave the system forever. The system parameters depend on the state of the random environment. The ergodicity condition is derived. The formulas for calculating the main performance measures of the system are obtained. The Laplace-Stieltjes transforms of waiting and sojourn times of a customer in the system are calculated.

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