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

Chesoong Kim; Alexander Dudin; Sergey Dudin; Olga Dudina

International Journal of Applied Mathematics and Computer Science (2014)

  • Volume: 24, Issue: 3, page 485-501
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Chesoong Kim, et al. "Analysis of an MMAP/PH₁,PH₂/N/∞ queueing system operating in a random environment." International Journal of Applied Mathematics and Computer Science 24.3 (2014): 485-501. <http://eudml.org/doc/271894>.

@article{ChesoongKim2014,
abstract = {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.},
author = {Chesoong Kim, Alexander Dudin, Sergey Dudin, Olga Dudina},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {random environment; marked Markovian arrival process; phase-type distribution; Laplace-Stieltjes transform},
language = {eng},
number = {3},
pages = {485-501},
title = {Analysis of an MMAP/PH₁,PH₂/N/∞ queueing system operating in a random environment},
url = {http://eudml.org/doc/271894},
volume = {24},
year = {2014},
}

TY - JOUR
AU - Chesoong Kim
AU - Alexander Dudin
AU - Sergey Dudin
AU - Olga Dudina
TI - Analysis of an MMAP/PH₁,PH₂/N/∞ queueing system operating in a random environment
JO - International Journal of Applied Mathematics and Computer Science
PY - 2014
VL - 24
IS - 3
SP - 485
EP - 501
AB - 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.
LA - eng
KW - random environment; marked Markovian arrival process; phase-type distribution; Laplace-Stieltjes transform
UR - http://eudml.org/doc/271894
ER -

References

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