Abstract:
We consider the 2-server queuing system with loss that admits requests during a time interval [0,T]. Players try to send their requests to the system, that provides a random access to its servers with some probabilities, and players know these probabilities. We consider a non-cooperative game for this queueing system. Each player's strategy is a time moment to send his request to the system trying to maximize the probability of successful service obtaining. We use a symmetric Nash equilibrium as an optimality criteria. Two models are considered for this game. In the first model the number of players is deterministic. In the second it follows a Poisson distribution. We prove that there exists a unique symmetric equilibrium for both models. Also we compare numerically equilibria for different models' parameters.
Citation:
Julia V. Chirkova, “Optimal arrivals to a two-server loss system with random access”, Mat. Teor. Igr Pril., 7:3 (2015), 79–111; Autom. Remote Control, 78:3 (2017), 557–580
\Bibitem{Chi15}
\by Julia~V.~Chirkova
\paper Optimal arrivals to a two-server loss system with random access
\jour Mat. Teor. Igr Pril.
\yr 2015
\vol 7
\issue 3
\pages 79--111
\mathnet{http://mi.mathnet.ru/mgta164}
\transl
\jour Autom. Remote Control
\yr 2017
\vol 78
\issue 3
\pages 557--580
\crossref{https://doi.org/10.1134/S0005117917030146}
Linking options:
https://www.mathnet.ru/eng/mgta164
https://www.mathnet.ru/eng/mgta/v7/i3/p79
This publication is cited in the following 9 articles:
Julia Chirkova, Vladimir Mazalov, “Equilibrium Arrivals to Preemptive Queueing System with Fixed and Random Population Size”, J. Oper. Res. Soc. China, 12:1 (2024), 77
Julia V. Chirkova, Lecture Notes in Computer Science, 13930, Mathematical Optimization Theory and Operations Research, 2023, 241
Julia V. Chirkova, Vladimir V. Mazalov, Lecture Notes in Computer Science, 13367, Mathematical Optimization Theory and Operations Research, 2022, 169
Leon Petrosyan, David Yeung, “Shapley value for differential network games: Theory and application”, JDG, 8:2 (2021), 151
Moshe Haviv, Liron Ravner, “A survey of queueing systems with strategic timing of arrivals”, Queueing Syst, 99:1-2 (2021), 163
Yu.V. Chirkova, “Optimal Arrivals in a Two-Server Rational Random-Access System with Loss”, Autom Remote Control, 81:7 (2020), 1345
Networking Games, 2019, 303
Vladimir V. Mazalov, Julia V. Chirkova, Networking Games, 2019, 211
Yuliya V. Chirkova, “Optimalnye obrascheniya k 2-servernoi sisteme s poteryami i ratsionalnym sluchainym dostupom”, MTIP, 8:3 (2016), 67–99
Citation in format AMSBIB
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