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

Satin, Yacov; Zeifman, Alexander; Sipin, Alexander; Ammar, Sherif I.; Sztrik, Janos

doi:10.3390/math8040594

Open AccessArticle

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

by

Yacov Satin

¹,

Alexander Zeifman

^2,3,4,*

,

Alexander Sipin

¹,

Sherif I. Ammar

^5,6

and

Janos Sztrik

⁷

¹

Department of Mathematics, Vologda State University, 160000 Vologda, Russia

²

Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia

³

Institute of Informatics Problems of the Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, 119333 Moscow, Russia

⁴

Vologda Research Center of the Russian Academy of Sciences, 160014 Vologda, Russia

⁵

Department of Mathematics, Faculty of Science, Menofia University, Shebin El Kom 32511, Egypt

⁶

Department of Mathematics, College of Science, Taibah University, Medinah 414111, Saudi Arabia

⁷

Department of Information Technology Systems and Networks, University of Debrecen, 4032 Debrecen, Hungary

^*

Author to whom correspondence should be addressed.

Mathematics 2020, 8(4), 594; https://doi.org/10.3390/math8040594

Submission received: 15 March 2020 / Revised: 8 April 2020 / Accepted: 9 April 2020 / Published: 15 April 2020

(This article belongs to the Special Issue Queueing Methods in Reliability Theory and Information Technology Systems)

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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

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MDPI and ACS Style

Satin, Y.; Zeifman, A.; Sipin, A.; Ammar, S.I.; Sztrik, J. On Probability Characteristics for a Class of Queueing Models with Impatient Customers. Mathematics 2020, 8, 594. https://doi.org/10.3390/math8040594

AMA Style

Satin Y, Zeifman A, Sipin A, Ammar SI, Sztrik J. On Probability Characteristics for a Class of Queueing Models with Impatient Customers. Mathematics. 2020; 8(4):594. https://doi.org/10.3390/math8040594

Chicago/Turabian Style

Satin, Yacov, Alexander Zeifman, Alexander Sipin, Sherif I. Ammar, and Janos Sztrik. 2020. "On Probability Characteristics for a Class of Queueing Models with Impatient Customers" Mathematics 8, no. 4: 594. https://doi.org/10.3390/math8040594

APA Style

Satin, Y., Zeifman, A., Sipin, A., Ammar, S. I., & Sztrik, J. (2020). On Probability Characteristics for a Class of Queueing Models with Impatient Customers. Mathematics, 8(4), 594. https://doi.org/10.3390/math8040594

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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

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