A random elastic traffic equilibrium problem via stochastic quasi-variational inequalities

The aim of the paper is to introduce a random elastic traffic equilibrium problem in a Hilbert space setting. The equilibrium condition is expressed by a random extension of the elastic Wardrop principle. Its characterization with a stochastic quasi -variational inequality is proved. Under suitable assumptions, the existence of a random equilibrium distribution is established. Furthermore, a numerical scheme to compute the random elastic traffic equilibrium distribution is presented. Finally a numerical example is discussed.