Before revision:  This upper bound allows providing a tight approximation of the Age of Information with a very low complexity  .
After revision:  This upper bound allows providing a tight approximation of the Age of Information with a very low complexity . We then provide a game framework that allows each source to determine its best probabilistic routing decision. By using Mean Field Games, we provide an analysis of the routing game framework, propose an efficient iterative method to find the routing decision of each source and prove its convergence to the desired equilibrium .