The (static) traffic assignment (TA) problem, which computes network equilibrium flows from origin–destination (OD) demand under flow conservation, is central to transportation modeling. As multimodal transportation systems (MTSs) grow, sharing detailed OD data – such as trip counts, timestamps, and routes – raises serious privacy concerns. Differential privacy (DP) has emerged as the leading standard for releasing such data, offering adjustable protection beyond traditional anonymization. However, current methods mostly apply extrinsic DP by adding noise to aggregate OD matrices before release, without fully addressing its effects on traffic modeling. This reveals TA’s unpreparedness for privacy-protected data and calls for redesigned methods that operate reliably under such constraints. To fill this gap, we propose the privacy-preserving traffic assignment (PPTA) framework, which embeds DP intrinsically within the TA process. Instead of externally perturbing aggregate demand, PPTA injects structured noise at the individual trip level. This preserves privacy while ensuring equilibrium feasibility through chance-constrained optimization, unifying privacy protection and traffic assignment. The framework supports various discrete choice models and noise types, using a moment-based approximation to boost computational efficiency. Our results show PPTA attains a privacy-utility balance beyond extrinsic methods, enabling robust, privacy-aware multimodal routing, network design, and pricing.

At present, the market share of ridesharing in China is relatively low, and there is still huge potential to be fully tapped in alleviating traffic congestion and reducing energy consumption and emissions. Incentive-based traffic demand management strategies can promote people’s willingness of ridesharing, but the design of incentive schemes is highly correlated with the market penetration of ridesharing. An unreasonable incentive scheme may easily lead to increased cost or even project failure. In order to further stimulate the potential ridesharing demand and make reasonable use of transportation resources, a road segment-based incentive optimization model for ridesharing is proposed, which uses ridesharing as the fulcrum and rewards as the lever to reduce the total social travel cost. The upper model of the proposed model aims to find the optimal incentive scheme to minimize the total social travel cost, and the lower model is a user equilibrium allocation model of ridesharing vehicles and single-driver vehicles under the incentive scheme. The iterative algorithm combining the genetic algorithm and the Frank-Wolfe algorithm is used to solve the upper and lower models, respectively, and the feasibility and effectiveness of the model are verified by using the Sioux Falls and Nguyen Dupuis transportation networks as numerical examples. The results show that budget investments that do not meet market penetrations may result in a significant increase in total social travel costs; and that, under the optimal incentive scheme, the total social travel cost is reduced by about 24.53%, the congestion of 50% of congested links is alleviated, and the fairness issue in traffic demand management is alleviated to a certain extent. Thus, there comes to the conclusion that the proposed model can provide theoretical support for managers to set up scientific and reasonable incentive-based ridesharing schemes.

The stochastic fundamental diagram (SFD), which describes the stochasticity of the macroscopic relations of traffic flow, plays a crucial role in understanding the uncertainty of traffic flow evolution and developing robust traffic control strategies. Although many efforts have been made to reproduce the SFD via various methods, few studies have focused on the analytical modeling of the SFD, particularly linking the macroscopic relations with microscopic behaviors. This study fills this gap by proposing a general micro-macroscopic modeling approach, which uses probabilistic leader–follower behavior to derive the macroscopic relations of a platoon and is referred to as the leader–follower conditional distribution-based stochastic traffic modeling (LFCD-STM) framework. Specifically, we first define a conditional probability distribution of speed for the leader‒follower pair according to Brownian dynamics, which is proven to be a general representation of the longitudinal interaction and compatible with classical car-following models. As a result, we can describe the joint distribution of vehicle speeds of the platoon through Markov chain modeling and further derive the macroscopic relations (e.g., the mean flow‒density relation and its variance) under equilibrium conditions. On the basis of this general micro-macroscopic framework, we utilize the maximum entropy approach to theoretically derive the SFD model, in which we provide a specific conditional distribution for longitudinal interaction and thus solve the analytical functions of the mean and variance of FD. The performance of the maximum entropy-based SFD model is thoroughly validated with the NGSIM I-80, US-101 and HighD datasets. The high consistency between the theoretical results and empirical results demonstrates the soundness of the LFCD-STM framework and the maximum entropy-based SFD model. Finally, the proposed SFD model has practical implications for promoting smoother driving behaviors to suppress stochasticity and improve traffic flow.