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

We consider the 2-server queueing loss-type system which admits requests during a time interval $[0,T]$. Players try to send their requests into the system, which randomly redirects each request to one of its free servers with some probabilities, or to unique free server, or refuses the request. We consider a non-cooperative game for this queuing 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. We compare numerically equilibria for different model parameters of the model. Also we compare an efficiency for the one-server model and the two-server model with a random access where the system has no information about servers' being busy.