On the approximation of queue-length distributions in transportation networks

Abstract: This paper focuses on the analytical probabilistic modeling of vehicular traffic. It formulates a stochastic 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 urban 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. Compared to the probabilistic link model of Lu and Osorio (2018) with an exogenous node model and a benchmark deterministic network loading model, the proposed network model derives signal plans with better performance. The case study highlights the added value of using between-link (i.e., across-node) interaction information for traffic management and accounting for stochasticity in the network.