Modeling of the market penetration of advanced traveler information systems using a mixed network equilibrium model

We consider a specific Advanced Traveler Information System (ATIS) whose objective is to reduce drivers' time uncertainty with recurrent network congestion through provision of traffic information to drivers. Suppose drivers who are equipped with an ATIS will receive complete information, and hence be able to find the minimum travel time routes in a user-optimal manner, while drivers who are not equipped with an ATIS will have only incomplete information, and hence may take longer travel time routes in a stochastic manner. We propose a convex programming model and an algorithm to solve this mixed behavior equilibrium problem for any given level of market penetration of ATIS. Furthermore, suppose that the information benefit received by a driver who buys an ATIS is measured as the travel time saving (stochastic mean travel time minus deterministic minimum travel time in a mixed behavior equilibrium), and the market penetration of ATIS is determined by a continuous increasing function of the information benefit, then we have a variable, mixed behavior equilibrium model with endogenous market penetration in an ATIS environment. We establish the existence, uniqueness and stability of this performance and demand equilibrium of ATIS, and propose an iterative procedure to calculate the ATIS market penetration and the resulting equilibrium network flow pattern