Optimal Arrivals in a Two-Server Rational Random-Access System with Loss

This paper considers a two-server rational random-access system with loss that receives requests on a time interval [0, T]. The users (players) are sending their requests to the system; then the system provides a random access with given probabilities to one of two free servers or to a single free server, or rejects the request. We study the following noncooperative 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 service. The symmetric Nash equilibrium is selected 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 (a) to compare the equilibria under different parameter values and (b) to compare the efficiency of this two-server system with the one-server counterpart and also with the corresponding pure random-access model in which the system has no information about the states of servers (busy or free).