We consider a stochastic approach in order to define an
equilibrium model for a traffic-network problem.
In particular, we assume a Markovian behaviour of the users in their
movements throughout the zones of the traffic area. This assumption turns out
to be
effective at least in the context of urban traffic, where, in general, the users tend to
travel by choosing the path they find more convenient and not necessarily depending on the
already travelled part.
The developed model is a homogeneous Markov chain, whose
stationary
distributions (if any) characterize the equilibrium.