Analytical modelling of systems with a ticket queue

  • Olga S. Dudina Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

Abstract

A queuing system of MAP/GPH/N/K type as a model of a ticket queue is herein considered. It is assumed that arriving users, after receiving a service ticket (place in the queue), can leave the system with a probability based on the number of users in front of them if they find the queue too long. In addition, users may leave the system during waiting due to impatience. The system does not know about the presence (absence) of the called users for service and spends some time servicing them, even if the corresponding user has already left the system. The stationary distribution of the system under consideration is calculated. Formulas for finding the main characteristics of the system performance are given. The presented numerical experiment shows the possibility of using the results for optimisation purposes.

Author Biography

Olga S. Dudina, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics); leading researcher at the laboratory of applied probabilistic analysis, department of probability theory and mathematical statistics, faculty of applied mathematics and computer science

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Published
2024-07-23
Keywords: ticket queue, correlated arrival process, impatience customers, generalised phase-type distribution
How to Cite
Dudina, O. S. (2024). Analytical modelling of systems with a ticket queue. Journal of the Belarusian State University. Mathematics and Informatics, 2, 40-53. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/6314
Issue
No 2 (2024): Journal of the Belarusian State University. Mathematics and Informatics
Section
Probability Theory and Mathematical Statistics

Copyright (c) 2024 Journal of the Belarusian State University. Mathematics and Informatics

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