The effect of signalised intersections on dynamic traffic assignment solution stability

This article examines a continuous-flow analytic dynamic traffic assignment (DTA) model with consideration of isolated uncoordinated traffic signals. The dynamic network loading component of the DTA model relies on trajectories and anticipated arrival order to nodes in order to achieve consistency between flow propagation along routes and kinematic waves (physical queue) representation of single link traffic behaviour. We compare results between a model where queues with random arrivals and deterministic departure rates are captured by non-stationary cycle-to-cycle Markov chains, and a model where only exit capacity effects of traffic signals are considered. Numerical examples illustrate that overall the model with Markov chains behaves properly, and captures interesting impacts of random queuing traffic signal delays on route choice and network level DTA solutions. A particular focus of this article is the issue of solution stability and its relationship to model specification and discretisation. We discuss the connection between DTA models and general finite element models in this respect, particularly regarding lag options in the discrete form of the equilibrium condition. Our results regarding these options, known as 'forward' versus 'backward' Euler method, or as 'reactive' versus 'predictive' user-equilibrium, confirm previous findings. In addition, the results show that the model specification with Markov chain representation of traffic signals enhances solution instability, and exhibits spurious oscillations even if backward Euler method is used. The results suggest that longer route choice intervals reduce oscillations, contrary to the typical behaviour in finite element models where stability generally improves when the resolution is refined.