On Probability Characteristics for a Class of Queueing Models with Impatient Customers

Yacov Satin, Alexander Zeifman, Alexander Sipin, Sherif I. Ammar and Janos Sztrik
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Yacov Satin: Department of Mathematics, Vologda State University, 160000 Vologda, Russia
Alexander Zeifman: Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia
Alexander Sipin: Department of Mathematics, Vologda State University, 160000 Vologda, Russia
Sherif I. Ammar: Department of Mathematics, Faculty of Science, Menofia University, Shebin El Kom 32511, Egypt
Janos Sztrik: Department of Information Technology Systems and Networks, University of Debrecen, 4032 Debrecen, Hungary

Mathematics, 2020, vol. 8, issue 4, 1-15

Abstract: In this paper, a class of queueing models with impatient customers is considered. It deals with the probability characteristics of an individual customer in a non-stationary Markovian queue with impatient customers, the stationary analogue of which was studied previously as a successful approximation of a more general non-Markov model. A new mathematical model of the process is considered that describes the behavior of an individual requirement in the queue of requirements. This can be applied both in the stationary and non-stationary cases. Based on the proposed model, a methodology has been developed for calculating the system characteristics both in the case of the existence of a stationary solution and in the case of the existence of a periodic solution for the corresponding forward Kolmogorov system. Some numerical examples are provided to illustrate the effect of input parameters on the probability characteristics of the system.

Keywords: queueing models; non-stationary Markovian queueing model; approximation; impatient customers; probability characteristics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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