The maximization of the network throughput ensuring free flow conditions in traffic and transportation networks: Breakdown minimization (BM) principle versus Wardrop's equilibria

We have revealed general physical conditions for the maximization of the network throughput at which free flow conditions are ensured, i.e., traffic breakdown cannot occur in the whole traffic or transportation network. A physical measure of the network – network capacity is introduced that characterizes general features of the network with respect to the maximization of the network throughput. The network capacity allows us also to make a general proof of the deterioration of traffic system occurring when dynamic traffic assignment is performed in a network based on the classical Wardrop' user equilibrium (UE) and system optimum (SO) equilibrium.