Synchromodal transport operations frequently require rapid re-planning in response to uncertain terminal service times, yet such decisions are typically made by multiple carriers with heterogeneous objectives and decentralized control. This study investigates collaborative re-planning in synchromodal transport networks under service-time uncertainty from a multi-carrier perspective. We formulate the problem as a decentralized decision-making process in which carriers must coordinate re-planning actions while preserving individual rationality. To address this challenge, we propose a model-assisted multi-agent reinforcement learning (MARL) framework that combines heuristic plan generation with learning-based carrier coordination. An adaptive large neighborhood search (ALNS) heuristic is used to generate feasible candidate re-planning options, while carriers are modeled as learning agents that decide whether to accept or reject these options through a consensus mechanism. Rather than directly optimizing a centralized model, carriers learn acceptance policies based on local observations and realized outcomes, without requiring prior knowledge of service-time distributions. An event-triggered and regret-based learning scheme is introduced to align global delay mitigation with carrier-specific cost preferences under uncertainty. Extensive computational experiments on a realistic synchromodal transport network demonstrate that the proposed framework significantly improves re-planning performance compared with benchmark strategies. The results show that decentralized, heterogeneous multi-agent coordination can outperform centralized and homogeneous approaches, particularly in scenarios with high uncertainty and avoidable delays. Mechanism and ablation analyses further reveal the structural importance of multi-agent decomposition, carrier heterogeneity, and the temporal allocation of decision preferences along the transport chain. Additional analyses examine sensitivity to key reward hyperparameters and negotiation round limits, robustness under alternative disruption distributions and network-graph perturbations, and controlled extension settings with more carriers and transshipments. The proposed approach provides a practical decision-support methodology for collaborative synchromodal transport re-planning under uncertainty.

This paper proposes a multilane traffic flow model based on the notions of conservation laws in Lagrangian coordinates. Both continuous formulation and discretization of the model are derived explicitly considering lane-changing characteristics. For model discretization, a lane-changing number estimation model is developed to calculate the net lane-changing number for each vehicle group considering the relative position between vehicle groups in the current and adjacent lanes. With model discretization, the spacing of vehicle groups for each lane can be dynamically calculated. In addition, the boundary conditions for both the continuous Lagrangian model and its discretization are also derived. A numerical implementation of the model in the case of a three-lane highway section with a lane-drop is discussed, and results indicate that the proposed Lagrangian model can well simulate traffic dynamics, including the generation and propagation of congestion, and the perturbation caused by lane-changing behaviors. The lane-changing characteristics in terms of a cumulative net number of lane-changing vehicles for each lane, and the spacing dynamics of vehicle groups can be estimated as well. We further validate the proposed model using real-world data observed from a two-lane freeway section in Japan. The results show that the proposed multilane Lagrangian model can well capture traffic dynamic properties and could provide a relatively accurate estimation in terms of lane volume dynamics, vehicle spacing dynamics, and the cumulative net number of lane-changing vehicles. Comparisons with the Eulerian multilane model indicate that the Lagrangian model offers superior performance in predicting vehicle counts and spacing, especially under congested conditions. This improved performance can be attributed to the Lagrangian model's capability to track individual vehicle groups, resulting in a more precise representation of traffic dynamics.

Dynamic multimodal transport planning is vital for enhancing flexibility and responsiveness in emergency logistics. We propose a dynamic planning approach that integrates drones into the multimodal system with trains, trucks, and aircraft, introducing dual-role drones that can be transported as cargo and later operate as carriers. A Mixed Integer Programming (MIP) model, optimized via a rolling horizon approach, supports real-time route planning. Given the problem’s complexity, we develop an Adaptive Large Neighborhood Search (ALNS) algorithm with problem-specific operators. The model accounts for mode coordination, routing constraints, and cargo heterogeneity. It dynamically replans routes under disruptions such as road damage, considering mode availability and delivery requirements. Numerical experiments are conducted based on a real disaster scenario. A comparison with an exact method shows improved computational efficiency and solution quality. Further comparisons with a drone-free and static approach highlight gains in service rate and disruption resilience. We also examine the impact of cargo heterogeneity. These results, across instances from 5 to 400 orders, provide practical insights for optimizing drone deployment, transport mode selection, and cargo management in disaster response.

This review aims to explore the potential for synchromodal transport planning at the operational level. Synchromodal transport planning involves the optimization of the movement of freights across multiple transport modes, with the objective of minimizing cost, improving efficiency, and promoting sustainability. Through this review, we provide a roadmap for methodological developments in the area of operational synchromodal transport planning research. The roadmap provides a comprehensive categorization of different fields and their trends. The fundamentals of synchromodal transport planning are evolved to more flexible planning approaches that take practical considerations and multiple objectives into account. Dynamic planning is evolving to become more adaptive and resilient to changing environments. Finally, collaborative planning will continue to integrate both vertical and horizontal collaboration with distributed optimization approaches. With dynamic and collaborative approaches considering preferences, the full potential of synchromodal transport planning can be unlocked towards efficient and sustainable freight transportation.

This paper proposes a multilane traffic flow model based on the notions of conservation laws in Lagrangian coordinates. Both the mathematical formulation and the graphical representation are provided. A logit choice model is applied to describe drivers' lane choice probability. The lane changing rate is estimated by employing the Incremental Transfer (IT) principle and the lane choice probability model. The numerical implementation of the model in the case of two lanes is discussed. The simulation results reveal that the proposed Lagrangian model is able to describe lane changing dynamics of vehicle platoons; while the lane changing equilibrium curve at the macroscopic level is consistent with that from the multilane Eulerian model as well as the observed data on the highway.

Urban travel times are rather variable as a result of a lot of stochastic factors both in traffic flows, signals, and other conditions on the infrastructure. However, the most common way both in literature and practice is to estimate or predict only expected travel times, not travel time distributions. By doing so, it fails to provide full insight into the travel time dynamics and variability on urban roads. Another limitation of this common approach is that the effect of traffic measures on travel time reliability cannot be evaluated. In this paper, an analytical travel time distribution model is presented especially for urban roads with fixed-time controlled intersections by investigating the underlying mechanisms of urban travel times. Different from mean travel time models or deterministic travel time models, the proposed model takes stochastic properties of traffic flow, stochastic arrivals and departures at intersections, and traffic signal coordination between adjacent intersections into account, and therefore, is able to capture the delay dynamics and uncertainty at intersections. The queue spillback phenomenon is explicitly taken into account by applying shockwave theory in a probabilistic way. The proposed model was further validated with both VISSIM simulation data and field GPS data collected in a Chinese city. The results demonstrate that the travel time distributions derived from the analytical model can well represent those from VISSIM simulation. The comparison with field GPS data shows that the model estimated link and trip travel time distributions can also represent the field travel time distributions, though a small discrepancy can be observed in both middle range travel times and higher travel times.

The importance of travel time reliability in traffic management, control, and network design has received a lot of attention in the past decade. In this paper, a network travel time distribution model based on the Johnson curve system is proposed. The model is applied to field travel time data collected by Automated Number Plate Recognition (ANPR) cameras. We further investigate the network-level travel time reliability by connecting the network reliability measures such as the weighted standard deviation of travel time rate and the weighted skewness of travel time rate distributions with network traffic characteristics (e.g., the network density). The weighting is done with respect to the number of signalized intersections on a trip. A clear linear relation between the weighted average travel time rate and the weighted standard deviation of travel time rate can be observed for different time periods with time-varying demand. Furthermore, both the weighted average travel time rate and the weighted standard deviation of travel time rate increase monotonically with network density. The empirical findings of the relation between network travel time reliability and network traffic characteristics can be possibly applied to assess traffic management and control measures to improve network travel time reliability.

The decision making of travelers for route choice and departure time choice depends on the expected travel time and its reliability. A common understanding of reliability is that it is related to several statistical properties of the travel time distribution, especially to the standard deviation of the travel time and also to the skewness. For an important corridor in Changsha (P.R. China) the travel time reliability has been evaluated and a linear model is proposed for the relationship between travel time, standard deviation, skewness, and some other traffic characteristics. Statistical analysis is done for both simulation data from a delay distribution model and for real life data from automated number plate recognition (ANPR) cameras. ANPR data give unbiased travel time data, which is more representative than probe vehicles. The relationship between the mean travel time and its standard deviation is verified with an analytical model for travel time distributions as well as with the ANPR travel times. Average travel time and the standard deviation are linearly correlated for single links as well as corridors. Other influence factors are related to skewness and travel time standard deviations, such as vehicle density and degree of saturation. Skewness appears to be less well to explain from traffic characteristics than the standard deviation is.