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Title: A New Method for Markovian Adaptation of the Non-Markovian Queueing System Using the Hidden Markov Model
Authors: Tanackov, Ilija
Prentkovskis, Olegas
Jevtić, Žarko
Stojić, Gordan
Ercegovac, Pamela
Keywords: queueing
Issue Date: 2019
Publisher: MDPI
Citation: Tanackov, I.; Prentkovskis, O.; Jevtić, Ž.; Stojić, G.; Ercegovac, P. A New Method for Markovian Adaptation of the Non-Markovian Queueing System Using the Hidden Markov Model. Algorithms 2019, 12, 133.
Series/Report no.: 12;7
Abstract: This manuscript starts with a detailed analysis of the current solution for the queueing system M/Er/1/∞. In the existing solution, Erlang’s service is caused by Poisson’s arrival process of groups, but not individual clients. The service of individual clients is still exponentially distributed, contrary to the declaration in Kendall’s notation. From the related theory of the Hidden Markov Model (HMM), for the advancement of queueing theory, the idea of “hidden Markov states” (HMS) was taken. In this paper, the basic principles of application of HMS have first been established. The abstract HMS states have a catalytic role in the standard procedure of solving the non-Markovian queueing systems. The proposed solution based on HMS exceeds the problem of accessing identical client groups in the current solution of the M/Er/r queueing system. A detailed procedure for the new solution of the queueing system M/Er/1/∞ is implemented. Additionally, a new solution to the queueing system M/N/1/∞ with a normal service time N(μ, σ) based on HMS is also implemented.
Description: This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making
ISSN: 1999-4893
Appears in Collections:Moksliniai straipsniai / Research articles

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