A general framework for nonlocal traffic flow models on networks

Tolls for Dynamic Equilibrium Flows

A duality-based characterization of implementability of dynamic edge flows for the multi-source, multi-destination case and a non-trivial proof that this assumption is always fulfilled for finitely supported edge flows with costs representing weighted travel times are provided.

Cooperative Route Guidance and Flow Control for Mixed Networks Comprising Expressway and Arterial Network

To address the limitations of existing models for mixed networks comprising expressways and arterial regions, this study develops a unified modeling and control framework. First, within such a mixed network, the trip length characteristics of urban trips are analyzed, revealing marked differences in trip lengths between trips leaving the network via arterial regions and those leaving via expressways through on-ramps. This heterogeneity is incorporated into the modeling process to reflect realistic travel patterns. Second, a hybrid traffic model is proposed by integrating a multi-class cell transmission model (CTM) for expressways with a combination of trip-based and accumulation-based macroscopic fundamental diagrams (MFDs) for urban regions. The trip-based MFD captures flow heterogeneity through remaining distance distributions, while the accumulation-based formulation enables tractable control. This integration ensures consistent route-based state representation across subsystems. Third, a route choice model is established, and a coordinated control strategy is developed under a model predictive control (MPC) framework, jointly optimizing route guidance, ramp metering, and perimeter control. The case study demonstrates that the proposed cooperative strategy effectively alleviates congestion and enhances network efficiency compared with flow control alone, with its performance further influenced by the level of compliance. Note to Practitioners—Mixed networks composed of urban arterials and expressways are widespread in cities. Because the two subsystems are coupled through ramps, the mechanisms of congestion become more complex and harder to manage; existing practice often manages the two networks separately, making it difficult to balance pressure at the overall network level in a timely manner. This paper proposes a coordinated method of route guidance and flow control for mixed networks. First, an integrated traffic model is established to characterize the dynamics of each urban region and expressway segment and the flow exchanges between subsystems, providing operators with a unified basis for understanding system states and interactions. On this basis, a coordinated route guidance and flow control scheme is introduced to mitigate congestion: route guidance allocates travel demand at origins to optimize the spatial distribution of flows across the network, while boundary flow control-implemented via ramp metering and perimeter control-dynamically regulates flow exchange between expressways and urban regions. For implementation, ramp metering and perimeter control can be deployed using existing signal controllers or ramp signals, and route guidance can be disseminated through navigation platforms or traveler information systems. A case study on a real network shows that, compared with flow control alone, the coordinated strategy further reduces network congestion and alleviates boundary queuing. The effectiveness of the method depends on network-specific calibration of trip-length distributions and on driver compliance with guidance. Future work may extend the study to intercity freeway corridors to further examine applicability under different spatial scales and demand structures.

Link-Based Multimodal Traffic Dynamics Model in Continuous-Time Framework

Computationally efficient models for multimodal traffic flows with inter-modal interactions are foundational for coordinated traffic management. However, such models are lacking in the current literature. This study introduces a multimodal link transmission model (M-LTM) accommodating both continuous road traffic and discrete tramway traffic at the network level. M-LTM builds on a link model that captures the inter-modal interactions through the moving bottleneck theory. We further develop node models describing the flow transfer, tram operations, and mode interactions at tram stops and intersections. Specifically, the tram dwell process and dwell-induced congestion of road traffic are simulated at the stop node, and the intersection node model can reproduce queue spillback and tram priority. Case studies are conducted on two synthetic one-node networks, a synthetic arterial network, and the real network of Dresden to demonstrate the predictive power and the applicability of the proposed model in network traffic analysis and management. The GEH statistics of road traffic are below 4, and the average tram arrival time absolute errors are less than 10 seconds.

The impact of the path ensemble on path percolation

A generalised path-percolation framework is introduced where paths are drawn from a temperature-controlled routing ensemble interpolating between geodesic and noisy transport, clarifying how microscopic routing organisation shapes macroscopic resilience, and identifying path elongation as a measurable precursor of failure in communication and transport infrastructure.

Simulation Modelling Practice and Theory

A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits

This paper introduces a multi-class extension of a discrete-velocity kinetic traffic flow model based on a non-local Prigogine-Herman framework. We derive a hyperbolically scaled system of equations from a continuous kinetic formulation describing interactions between different vehicle classes through braking and relaxation terms. The model is then discretized with respect to the velocity variable for an arbitrary number of vehicle classes, and the structural properties of the resulting formulation are analyzed. In particular, we prove hyperbolicity and total linear degeneracy. Due to the non-conservative structure of the model, we employ a path-conservative finite volume scheme for the numerical approximation of the system. Finally, we derive the corresponding diffusively-corrected macroscopic multi-class model, investigate its stability and present numerical simulations on a single-lane road to illustrate the theoretical findings.