Analysis of a multi-server system with Markovian arrival process and dynamic pricing

Authors

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

Keywords:

dynamic pricing, Markovian arrival process, admission control, server vacation policy, ride-hailing platform

Abstract

This paper presents a mathematical model of a multi-server queuing system which integrates a Markovian arrival process (MAP) with an adaptive admission control mechanism based on dynamic pricing and a comprehensive server vacation policy. By formulating the system dynamics as a three-dimensional continuous-time Markov chain, we derive its infinitesimal. We provide explicit formulas for key performance measures, including average numbers of active and busy servers, and loss probabilities. Numerical experiments demonstrate that the synergy between dynamic pricing and resource management is crucial for balancing the quality of service and operational efficiency. Furthermore, we identify an optimal pricing strategy that maximises the system’s economic profit by managing the trade-off between congestion and customer rejection.

Author Biographies

  • 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

  • Sergei A. Dudin, 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

2026-09-25

Issue

No. 2 (2026): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics

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How to Cite

[1]
Dudina, O.S. and Dudin, S.A. 2026. Analysis of a multi-server system with Markovian arrival process and dynamic pricing. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Sep. 2026), 97–109.