Nash equilibria for combined flow control and routing in networks: asymptotic behavior for a large number of users

We consider a combined routing and flow control problem involving multiple links, and a large number of noncooperative users, with the utility function of each user quantifying a trade-off between throughput and delay. We study the existence and characterization of `approximate´ Nash equilibria of the symmetric type when the number of users gets arbitrarily large, and demonstrate that there may not exist an approximate equilibrium with positive flow on all links. We also provide a complete set of results for the single user multiple link problem