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

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.