<abstract xmlns="http://www.w3.org/1999/xhtml"> 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</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

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

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

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Analysis of an  queueing system operating in a random environment

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...

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

Published Online: Sep 25, 2014

Page range: 485 - 501

Received: Aug 19, 2013

DOI: https://doi.org/10.2478/amcs-2014-0036

Keywords
random environment, marked Markovian arrival process, phase-type distribution, Laplace-Stieltjes transform

© by Chesoong Kim

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 25, 2014

Page range: 485 - 501

Received: Aug 19, 2013

DOI: https://doi.org/10.2478/amcs-2014-0036

Keywordsrandom environment, marked Markovian arrival process, phase-type distribution, Laplace-Stieltjes transform

© by Chesoong Kim

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Keywords
random environment, marked Markovian arrival process, phase-type distribution, Laplace-Stieltjes transform