A probabilistic traffic-theoretic network loading model suitable for large-scale network analysis

This paper formulates an analytical stochastic network loading model. It is a stochastic formulation of the link transmission model (LTM), which itself is an operational formulation of Newell’s simplified theory of kinematic waves. The proposed model builds upon the initial model of Osorio and Flötteröd (2015). It proposes a formulation with enhanced scalability. In particular, compared to the initial model, it has a complexity that is linear, rather than cubic, in the link’s space capacity. This makes it suitable for large-scale network analysis. The model is validated versus a simulation-based implementation of the stochastic LTM. The proposed model yields significant gains in computational efficiency, while preserving accuracy. The validation experiments illustrate how computational runtimes of the proposed model increase linearly with the link’s space capacity, while the initial model has an exponential increase in runtimes. The proposed model yields accurate distributional approximations of the link’s boundary conditions. It is used to address a probabilistic formulation of a city-wide signal control problem. The model is shown to be robust to the quality of the initial signal plans. It yields signal plans that systematically outperform both initial plans, as well as a plan derived by a widely used commercial signal control software. The model is suitable for large-scale network optimization.