Geodesic
Symmetric Nash equilibrium arrivals to queuing system
Contributions to game theory and management, Tome 16 (2023), pp. 53-60.

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We consider a game-theoretic setting for the queuing system models where input process of arrivals is strategic. This paper generalizes a methodology for the symmetric Nash equilibrium exploring in queuing system with loss. We assume that the system admits customer requests at the time interval $[0,T]$. Each of customers chooses the moment to send his request into the system maximizing his payoff. Several models of certain systems are presented as examples demonstrating a result of the methodology application.
Keywords: queueing system, strategic customers, optimal arrivals, Kolmogorov backward equations, Nash equilibrium. 
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     author = {Julia V. Chirkova},
     title = {Symmetric {Nash} equilibrium arrivals to queuing system},
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Julia V. Chirkova. Symmetric Nash equilibrium arrivals to queuing system. Contributions to game theory and management, Tome 16 (2023), pp. 53-60. http://geodesic.mathdoc.fr/item/CGTM_2023_16_a3/

[1] Altman, E., Shimkin, N., “Individually optimal dynamic routing in a processor sharing system”, Oper. Res., 46 (1998), 776–784 | DOI | Zbl

[2] Breinbjerg, J., Platz, T. T., Østerdal, L. P., Equilibrium Arrivals to a Last-come First-served Preemptive-resume Queue, Working Papers 17-2020, Copenhagen Business School, Department of Economics, 2022 https://ideas.repec.org/p/hhs/cbsnow/2020_017.html

[3] Chirkova, Yu. V., “Optimal Arrivals in a Two-Server Rational Random-Access System with Loss”, Automation and Remote Control, 81:7 (2020), 1345–1365 | DOI | MR | Zbl

[4] Chirkova, Yu. V., “Optimal arrivals in a two-server random access system with loss”, Automation and Remote Control, 78:3 (2017), 557–580 | DOI | MR

[5] Chirkova, J. V., Mazalov, V. V., “Optimal Arrivals to Preemptive Queueing System”, Mathematical Optimization Theory and Operations Research, 21st International Conference, MOTOR 2022, Proceedings (Petrozavodsk, Russia, July 2–6, 2022), Lecture Notes in Computer Science, 13367, Springer, Cham, 2022, 169–181 | DOI | MR | Zbl

[6] Chirkova, J. V., “Equilibrium Arrivals to Preemptive Queueing System with Fixed Reward for Completing Request”, Mathematical Optimization Theory and Operations Research, MOTOR 2023, Lecture Notes in Computer Science, 13930, Springer, Cham, 2023 | MR | Zbl

[7] Glazer, A., Hassin, R., “?/M/1: On the equilibrium distribution of customer arrivals”, Eur. J. Oper. Res., 13 (1983), 146–150 | DOI | MR | Zbl

[8] Hassin, R., Kleiner, Y., “Equilibrium and optimal arrival patterns to a server with opening and closing times”, IIE Trans., 43 (2011), 164–175 | DOI

[9] Haviv, M., “When to arrive at a queue with tardiness costs”, Perform. Eval., 70 (2013), 387–399 | DOI

[10] Haviv, M., Ravner, L., “A survey of queueing systems with strategic timing of arrivals”, Queueing Syst., 99 (2021), 163–198 | DOI | MR

[11] Jain, R., Juneja, S., Shimkin, N., “The concert queueing game: To wait or to be late”, Discret. Event Dyn. Syst., 21 (2011), 103–138 | DOI | MR | Zbl

[12] Mazalov, V. V., Chuiko, J. V., “Nash equilibrium in the optimal arrival time problem”, Comput. Technol., 11 (2006), 60–71

[13] Ravner, L., Haviv, M., “Strategic timing of arrivals to a finite queue multi-server loss system”, Queueing Syst., 81 (2015), 71–96 | DOI | MR | Zbl

[14] Ravner, L., Haviv, M., “Equilibrium and Socially Optimal Arrivals to a Single Server Loss System”, Int. Conf. on Network Games Control and Optimization 2014 (NETGCOOP'14) (Trento, Italy, October 2014) | MR

[15] Teraoka, Y., Hohjo, H., “N-person silent game on sale”, Scientiae Mathematicae Japonicae, 63:2 (2006), 237–240 | MR | Zbl