Stability of equilibrium points of traffic networks under constant input flows and splitting rates

In this paper, a multi-destination multi-source traffic network of a single kind of vehicles is considered. In particular, an analysis of the system model in steady-state conditions has been performed both as regards the input flows from the external and the splitting rates. It has been investigated under which conditions the system admits a unique asymptotically stable equilibrium point under Lyapunov's indirect method. The condition that will be described has a very clear physical significance and it represents an interesting insight about the way by which the unique asymptotically stable equilibrium point can be found analytically when the information about the external inputs, the values of the splitting rates, and the parameters characterizing each link in the network are made available.