Self-Service System with Rating Dependent Arrivals

Alexander Dudin, Olga Dudina, Sergei Dudin and Yulia Gaidamaka
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Alexander Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Olga Dudina: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Sergei Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Yulia Gaidamaka: Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia

Mathematics, 2022, vol. 10, issue 3, 1-21

Abstract: A multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encounter problems is considered as the model of real-world systems with customers’ self-service. Such systems are widely used in many areas of human activity. An arrival flow is assumed to be the novel essential generalization of the known Markov Arrival Process ( MAP ) to the case of the dynamic dependence of the parameters of the M A P on the rating of the system. The rating is the process defined at any moment by the quality of service of previously arrived customers. The possibilities of a customers immediate departure from the system at the entrance to the system and the buffer due to impatience are taken into account. The system is analyzed via the use of the results for multi-dimensional Markov chains with level-dependent behavior. The transparent stability condition is derived, as well as the expressions for the key performance indicators of the system in terms of the stationary probabilities of the Markov chain. Numerical results are provided.

Keywords: multi-server queueing model; rating; self-sufficient servers; self-checkout; assistants; multi-dimensional Markov chains (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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