Link transmission model: A formulation with enhanced compute time for large-scale network optimization

We formulate a traffic theoretic and probabilistic analytical link transmission model. The proposed model extends past work that is based on a stochastic formulation of the link transmission model, which itself is an operational formulation of Newell’s simplified theory of kinematic waves. The proposed model yields a probabilistic description of the link’s upstream and downstream boundary conditions. The model only tracks the transient probabilities of two of the link’s boundary states. This leads to a model with a state space dimension that is constant, i.e., it does not depend on any link attributes, such as link length. In other words, the model has constant complexity, whereas past formulations have a complexity that scales linearly or cubically with link length. The gain in computational runtime is of at least one order of magnitude and it increases with link length. This makes the proposed model suitable for large-scale network optimization. The model is validated versus a simulation-based implementation of the stochastic link transmission model. Its performance is also benchmarked with other past analytical formulations. The proposed model yields estimates with comparable accuracy, while the computational efficiency is enhanced by at least one order of magnitude. It is also validated versus a microscopic traffic simulator, the results indicate that the proposed model accurately approximates the link’s boundary conditions for realistic traffic situations, such as signalized links and platoon arrival patterns. The model is then used to address a city-wide traffic signal control problem. The performance of the proposed model is benchmarked versus various other models and traffic signal control approaches. It is shown to reduce optimization compute time by at least one order of magnitude, while also yielding solutions (i.e., signal plans) with improved performance.