A New Method for Markovian Adaptation of the Non-Markovian Queueing System Using the Hidden Markov Model
Ilija Tanackov,
Olegas Prentkovskis,
Žarko Jevtić,
Gordan Stojić,
Pamela Ercegovac
Affiliations
Ilija Tanackov
Faculty of Technical Sciences, University of Novi Sad, TrgDositejaObradovi’ca 6, 21 000 Novi Sad, Serbia
Olegas Prentkovskis
Department of Mobile Machinery and Railway Transport, Faculty of Transport Engineering, Vilnius Gediminas Technical University, Plytinėsg.27, LT-10105 Vilnius, Lithuania
Žarko Jevtić
Faculty of Technical Sciences, University of Novi Sad, TrgDositejaObradovi’ca 6, 21 000 Novi Sad, Serbia
Gordan Stojić
Faculty of Technical Sciences, University of Novi Sad, TrgDositejaObradovi’ca 6, 21 000 Novi Sad, Serbia
Pamela Ercegovac
Faculty of Technical Sciences, University of Novi Sad, TrgDositejaObradovi’ca 6, 21 000 Novi Sad, Serbia
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.
