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.
@article{bwmeta1.element.bwnjournal-article-amcv24i3p485bwm,
author = {Chesoong Kim and Alexander Dudin and Sergey Dudin and Olga Dudina},
title = {Analysis of an MMAP/PH1,PH2/N/[?] queueing system operating in a random environment},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {24},
year = {2014},
pages = {485-501},
zbl = {1322.60195},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv24i3p485bwm}
}
Chesoong Kim; Alexander Dudin; Sergey Dudin; Olga Dudina. Analysis of an MMAP/PH₁,PH₂/N/∞ queueing system operating in a random environment. International Journal of Applied Mathematics and Computer Science, Tome 24 (2014) pp. 485-501. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv24i3p485bwm/
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