Moment Approximation to a Markov Model of Binary Route Choice

The paper considers a discrete-time, Markov, stochastic process model of drivers' day-to-day evolving route choice, the evolving ‘state’ of such a system being governed by the traffic interactions between vehicles, and the adaptive behaviour of drivers in response to previous travel experiences. An approximating deterministic process is proposed, by approximating both the probability distribution of previous experiences—the “memory filter”—and the conditional distribution of future choices. This approximating process includes both flow means and variances as state variables. Existence and uniqueness of fixed points of this process are examined, and an example used to contrast these with conventional stochastic equilibrium models. The elaboration of this approach to networks of an arbitrary size is discussed.