Advanced traveller information systems under recurrent traffic conditions: Network equilibrium and stability

- Assignment model for networks with advanced traveller information systems (ATIS).
- Day-to-day dynamic process for modelling non-equilibrium transients.
- Existence, uniqueness and local stability of the equilibrium as a fixed-point state.
- Small values of ATIS market penetration are enough to ensure the stability.
- Small levels of ATIS inaccuracy does not disrupt the stability (numerically proved).

In this paper the stability of traffic equilibrium is analysed by using a framework where advanced traveller information systems (ATIS) are explicitly modelled. The role played by information in traffic networks is discussed, with particular reference to the day-to-day dynamics of the traffic network and to system stability at equilibrium. The perspective adopted is that of transportation planning under recurrent network conditions. The network is considered to be in equilibrium, viewed as a fixed-point state of a day-to-day deterministic process, here modelled as a time-discrete non-linear Markovian dynamic system. In discussing the effects generated by the introduction of ATIS, the paper examines: changes in the fixed point(s) with respect to the absence of ATIS, how the theoretical conditions for fixed-point existence and uniqueness are affected, and the impact on the stability properties and the stability region at equilibrium. Most of the analyses are carried out with explicit theoretical considerations. Moreover, a toy network is also employed to explore numerically the effects of removing some assumptions concerning the accuracy of ATIS.