Optimal arrivals in a two-server random access system with loss

This paper considers a two-server random access system with loss that receives requests on a time interval [0, T]. The users (players) send their requests to the system, and then the system provides a random access to one of its two servers with some known probabilities. We study the following non-cooperative game for this service system. As his strategy, each player chooses the time to send his request to the system, trying to maximize the probability of servicing. The symmetric Nash equilibrium acts as the optimality criterion. Two models are considered for this game. In the first model the number of players is deterministic, while in the second it obeys the Poisson distribution. We demonstrate that there exists a unique symmetric equilibrium for both models. Finally, some numerical experiments are performed to compare the equilibria under different values of the model parameters.