IP routing: user equilibrium versus system optimal

Routing has long been deemed as one of the most important problems in IP networks. We consider the strategies in IP networks. Two routing models are discussed, which correspond to two objectives of IP routing. The first model is user equilibrium (UE), this happens when different users select their shortest routes independently, most current routing algorithms in IP networks are based on this idea, i.e., find the shortest path for each packet. The second one is system optimal (SO), which is preferable to the service providers because its objective is to minimize the total network cost. These two models have been studied in transportation systems for many years, we found the basic ideas can also be used in data networks. We first introduced the resistance model on a link and on a path, on the basis of which the two routing models are discussed. The conditions at the optimal solution are also given. We further conclude that the two models are identical if the block effect of the network can be neglected.