A queueing system with heterogeneous impatient customers and consumable additional items

• Autorzy: Baek J. , Dudina O. , Kim C.

Identyfikatory

DOI

10.1515/amcs-2017-0026

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

marked Markovian arrival process; consumable additional items; phase type distribution; impatient customer

PL

Markowski proces zgłoszeń; system kolejkowy; rozkład fazowy; klient niecierpliwy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 2
• Strony: 367--384
• Opis fizyczny: Bibliogr. 25 poz., rys., tab., wykr.

Twórcy

autor

Baek J.

• Department of Industrial and Information Systems Engineering, Chonbuk National University, Jeonju, 54896, Republic of Korea

autor

Dudina O.

• Research Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4, Nezavisimosti Av., Minsk, 220030, Belarus; RUDN University, 6, Miklukho-Maklaya Str., Moscow, 117198, Russia

autor

Kim C.

• Department of Industrial Engineering, Sangji University, Wonju, Kangwon, 26339, Republic of Korea

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).