Analysis of an MMAP/PH₁, PH₂/N/∞ queueing system operating in a random environment

• Autorzy: Kim C. , Dudin A. , Dudin S. , Dudina O.

Identyfikatory

DOI

10.2478/amcs-2014-0036

• Języki publikacji: EN

Abstrakty

EN

A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. The criterion of ergodicity for a multi-dimensional Markov chain describing the behavior of the system and the algorithm for computation of its steady-state distribution are outlined. Some key performance measures are calculated. The Laplace–Stieltjes transforms of the sojourn and waiting time distributions of priority and non-priority customers are derived. A numerical example illustrating the importance of taking into account the correlation in the arrival process is presented.

Słowa kluczowe

EN

random environment; marked Markovian arrival process; phase type distribution; Laplace–Stieltjes transform

PL

rozkład fazowy; transformata Laplace'a-Stieltjesa; system operacyjny; system kolejkowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2014
• Tom: Vol. 24, no. 3
• Strony: 485--501
• Opis fizyczny: Bibliogr. 23 poz., rys., wykr.

Twórcy

autor

Kim C.

• Department of Business Administration, Sangji University, Wonju, Kangwon, 220-702, Korea

autor

Dudin A.

• Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus

autor

Dudin S.

• Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus

autor

Dudina O.

• Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus

Bibliografia

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