**5. Concluding remarks**

In this chapter, we presented a mathematical framework that provides a new insight for understanding the spread of traffic congestions in an urban network system. In particular, we considered a dynamical model, based on the well-known susceptible-infected-recovered (SIR) model from mathematical epidemiology, with small random perturbations, that describes the process of traffic congestion propagation and dissipation in an urban network system. Moreover, we also provided the asymptotic probability estimate based on the Freidlin-Wentzell theory of large deviations for certain rare events that are difficult to observe in the simulation of an urban traffic network dynamic, where such a framework provides a computational algorithm for constructing efficient importance sampling estimators for rare event simulations of certain events associated with the spread of traffic congestions in the traffic network.
