Stability of Traffic Equilibria in a Day-to-Day Dynamic Model of Route Choice and Adaptive Signal Control

Adaptive traffic signal control has the potential to promote the efficient use of road intersections, thus contributing to the effectiveness of urban traffic management schemes. However, the reaction of drivers to repeatedly updated signal settings and the ensuing route choice dynamics may trigger the emergence of various kinds of network instability. In this study, the joint evolution of traffic flows and adaptive signal settings in a road network is investigated at the level of day-to-day dynamics with an explicit focus on the stability issue. We show how a Logit form signal control policy can be used, in interaction with route choice, to counter the emergence of instabilities possibly arising as a consequence of various behavioral factors and network conditions. After providing a general formulation of the model as a discrete time, deterministic nonlinear dynamical system, an explicit analysis of fixed-point stability is carried out for a simple network. Numerical results obtained from the implementation of the model on two example networks are presented in order to support the analytical findings of this study. We conclude that, in an integrated traffic management and information system, a properly calibrated adaptive signal control policy has the potential to offset the destabilizing effect of highly accurate driver information supplied by navigational aids. Our findings also suggest that the Logit-like control policy performs better than the Equisaturation signal setting method, in terms of average intersection delay at equilibrium, for all levels of driver information and travel demand tested in the experiment.