On the approximation of queue-length distributions in large-scale urban networks

This paper focuses on the analytical probabilistic modeling of vehicular traffic. It formulates a node model. It then formulates a network model by coupling the node model with the link model of Lu and Osorio (2018), which is a stochastic formulation of the traffic-theoretic link transmission model. The proposed network model is scalable and computationally efficient, making it suitable for large-scale network optimization. For a network with $r$ links, each of space capacity $\ell$, the model has a complexity of $\mathcal{O}(r\ell)$. The network model yields the marginal distribution of link states. The model is validated versus a simulation-based network implementation of the stochastic link transmission model. The validation experiments consider a set of small network with intricate traffic dynamics. For all scenarios, the proposed model accurately captures the traffic dynamics. The network model is used to address a signal control problem. The case study highlights the added value of using between-link (i.e., across-node) interaction information for traffic management.