Analysis of single-server multi-class queue with unreliable service, batch correlated arrivals, customers impatience, and dynamical change of priorities

A single-server non-pre-emptive priority queueing system of a finite capacity with many types of customers is analyzed. Inter-arrival times can be correlated and batch arrivals are allowed. Possible unreliability of the server, implying the loss of a customer or the necessity of its service from the early beginning or some phase of the service, is taken into account. Initial priorities provided to various types of customers at the arrival moment can be varied (increased or decreased) after the random amount of time during the customer stay in the buffer. Such a type of queues arises in the modeling operation of various emergency care systems, information, and perishable goods delivering systems, etc. The stationary behavior of the system is described by the finite state multi-dimensional continuous-time Markov chain with the upper-Hessenberg block structure of the generator. The stationary distribution of the system states and some important characteristics of the system are calculated. The presented numerical examples illustrate opportunities to quantitatively evaluate the impact of the buffer capacity and customers’ mean arrival rate on the most important characteristics of the system. The possibility of solving optimization problems is briefly shown. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Авторы
Журнал
Издательство
MDPI AG
Номер выпуска
11
Язык
Английский
Статус
Опубликовано
Номер
1257
Том
9
Год
2021
Организации
  • 1 Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus
  • 2 Applied Mathematics and Communications Technology Institute, Peoples’ Friendship, University of Russia, (RUDN University), 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation
Ключевые слова
Batch marked Markov arrival process; Dynamic priority queue; Performance evaluation; Phase-type with failures time distribution
Дата создания
20.07.2021
Дата изменения
29.11.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/74248/
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