A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products, half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number of consumable additional items depending on the type of the customer. The service time has a phase-type distribution depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of optimization problems. © 2017 J. Baek et al.

Авторы
Baek J.1 , Dudina O. 2, 3 , Kim C.4
Издательство
Walter de Gruyter GmbH
Номер выпуска
2
Язык
Английский
Страницы
367-384
Статус
Опубликовано
Том
27
Год
2017
Организации
  • 1 Department of Industrial and Information Systems Engineering, Chonbuk National University, Jeonju, 54896, South Korea
  • 2 Research Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4, Nezavisimosti Av., Minsk, 220030, Belarus
  • 3 RUDN University, 6, Miklukho-Maklaya Str., Moscow, 117198, Russian Federation
  • 4 Department of Industrial Engineering, Sangji University, Wonju, Kangwon, 26339, South Korea
Ключевые слова
consumable additional items; impatient customers; marked Markovian arrival process; phase-type distribution
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5470/