Signal setting with demand assignment: Global optimization with day-to-day dynamic stability constraints.

This paper deals with traffic signal setting with demand assignment. All approaches proposed in literature to address this problem are based on equilibrium assignment, well established in literature as well as in practice. Still it is widely acknowledged that there are some relevant issues that may not be effectively addressed under the equilibrium approach, mainly uniqueness and stability, sensitivity to parameters and/or starting state. These issues should be better deal with a day-to-day dynamic approach, through deterministic (or stochastic) process models. This issue seems relevant since optimization of signal timings under equilibrium assumptions may not guarantee that an effective solution is obtained, because it may well be not an attractor of the evolution over time. The main contributions of this paper are: - a simple but still effective deterministic process models based on exponential smoothing filters, which also include effects of signal setting this model allows to state local stability of fixed-point states (consistent with equilibrium patterns) through the spectral analysis of the Jacobian matrix of the recursive equations modelling the evolution over time of the system; - an expression of equilibrium stability conditions that can be included as constraints within global optimization models for signal setting; such models guarantee that stability conditions are satisfied by obtained solution. Results from an application to a toy network, supporting major theoretical findings, are also reported. The very simple example allows for graphical representation to develop a general method useful to address implementation at real scale.