Chirkova, J.V., Mazalov, V.V.
Optimal Arrivals to Preemptive Queueing System
// Mathematical Optimization Theory and Operations Research. 21st International Conference, MOTOR 2022, Petrozavodsk, Russia, July 2–6, 2022, Proceedings. Lecture Notes in Computer Science, vol 13367. Springer, Cham, 2022. Pp. 169-181
Keywords: Queueing system, Preemptive access, Strategic users, Optimal arrivals, Kolmogorov backward equations, Nash equilibrium
This paper considers a single-server queueing system with strategic users in which customers (players) enter the system with preemptive access. As soon as the customer request enters the system, the server immediately starts the service. But when the next request arrives in the system, the previous one leaves the system even he has not finished his service yet. We study the following non-cooperative game for this service system. Each player decides when to arrive at the queueing system within a certain period of time. The objective of the player is to maximize the probability of receiving service. We show that there exists a unique symmetric Nash equilibrium in this game. Finally, some numerical experiments are carried out to compare the equilibria under different values of the model parameters.
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