Creator:
Kim, Chesoong ; Dudin, Alexander ; Dudin, Sergey ; Dudina, Olga
Contributor:
Abaev, Pavel - ed. ; Razumchik, Rostislav - ed. ; Kołodziej, Joanna - ed.
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Subject and Keywords:
random environment ; marked Markovian arrival process ; phase-type distribution ; Laplace-Stieltjes transform
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.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
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Source:
AMCS, volume 24, number 3 (2014) ; click here to follow the link