A mixed-behaviour equilibrium model under predictive and static Advanced Traveller Information Systems (ATIS) and state-dependent route choice

In transportation planning and design studies it is customary to consider the network in its equilibrium state. Equilibrium conditions in the presence of Advanced Traveller Information Systems (ATIS) and recurrent congestion have been formulated either according to some behavioural principle derived from Wardrop's assumption, or as fixed-point states of day-to-day dynamic assignment processes. In the latter approach only, a differentiation has been introduced between predictive ATIS and ATIS providing static information, but the impacts on equilibrium travel times are relatively unexplored. In addition, the route choice updating model is formulated without consideration of state-dependent effects, such as inertia to change. This forms the motivation for the present paper. According to traffic information sources, three classes of users are considered: (a) users with predictive information, (b) users with static information and compliant, (c) users not equipped with ATIS or noncompliant. Users of the three classes make choices in a stochastic manner based on a logit model subject to inertia. Users of the first class have lower perception variance in view of the higher information quality. The compliance rate is endogenous and dependent on the information accuracy of the static ATIS. The fixed points in the class-specific route flows of the dynamic day-to-day processes characterise a new concept of network equilibrium, referred to as Mixed User Equilibrium (MUE), where, if each user shifts from her currently used route to her newly chosen route, the observed class-specific route flows do not change. A variant of the method of successive averages is proposed for computing MUE. The model is illustrated by an example related to the Nguyen-Dupuis network. The impacts on equilibrium travel times of the market penetration of ATIS with different functionalities as well as of inertia are examined.