On the approximation of queue-length distributions in transportation networks

TL;DR

This paper introduces a scalable, probabilistic network model for vehicular traffic that accurately captures traffic dynamics and improves signal control strategies by incorporating stochastic interactions between links.

Contribution

It presents a novel, computationally efficient stochastic network model coupling node and link dynamics, validated against simulations, and demonstrates improved traffic management performance.

Findings

Model accurately captures traffic dynamics across scenarios.

Proposed model outperforms benchmark deterministic models.

Incorporates stochastic link interactions for better signal control.

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.