Mitigating Regional Traffic Congestion via School Start Time Scheduling: A Bilevel Alternating Optimization Approach

Dynamic Congestion Pricing in Distribution Networks via a Convex-Analytic Bilevel Reformulation

Dynamic congestion pricing is an important tool for managing congestion and coordinating distributed energy resources in active distribution networks. However, scalable mechanisms that preserve participant autonomy remain computationally challenging because the operator-resource interaction is naturally bilevel. This paper develops a convex-analytic framework in which a distribution system operator computes dynamic congestion-price adders, while decentralized energy hubs schedule flexible demand, storage, local generation, renewable curtailment, and grid import/export. Unlike conventional single-level reformulations that replace lower-level problems by Karush-Kuhn-Tucker (KKT) conditions, complementarity constraints, and big-M linearizations, the proposed model represents follower feasibility and optimality through a Fenchel-Young equality involving the convex conjugate of an extended follower objective. The remaining bilinear price-response term is handled through a penalized difference-of-convex reformulation and sequential convex approximation. The method solves continuous convex subproblems and avoids the constraint-wise complementarity and branch-and-bound scaling of mixed-integer KKT reformulations; its main computational drivers are price-response dimension and conjugate evaluation rather than binary encodings of follower inequalities. On augmented IEEE 13- and 34-node feeders, it reduces congestion by 96.89% and 96.45%, respectively, approaches centralized full-information dispatch, certifies price-response consistency to numerical precision, and yields lower residual congestion than time-limited KKT incumbents within the computational budget.

Addressing congestion in time-expanded networks: a lifeboat allocation model for maritime evacuations

This paper addresses the challenge of congestion in time-expanded networks, focusing on a case study related to maritime evacuations. The problem is made complex by an endogenous relationship between inputs and outputs, where the assignment of flow to an edge leads to increased congestion, which reflects in later arrivals and changes on the overall network topology. This dynamic interaction between flow and congestion is central to the problem, as it results in a feedback loop that complicates the identification of optimal evacuation paths. The study presents an iterative algorithm inspired by the network-simplex method, designed to handle the evolving nature of congestion while minimizing evacuation time. While the primary case study involves cruise ship evacuations, the approach is generalizable to other cases where congestion and nonlinear flow dynamics are significant factors. By considering lifeboat capacity, passenger mobility restrictions, and the impact of congestion on network structure, this work provides a practical initial plan for an evacuation off-shore, considering a congested, time-expanded network setting.

A Developed generalized mathematical traffic flow model for a single intersection

Efficient traffic management at urban intersections remains a major challenge due to increasing demand and complex network interactions. This paper presents a generalized mathematical traffic flow model for a signalized intersection that dynamically communicates with four neighbouring intersections (ahead, behind, left, and right). The model integrates a state-space representation to capture queue dynamics, arrival rates, and interconnection effects within a unified framework. A demand-driven signal control strategy is developed to allocate green time based on real-time vehicle demand, eliminating wasted signal phases. The framework further incorporates Internet of Things (IoT)-based sensing for real-time data acquisition and inter-intersection communication, alongside an Artificial Intelligence (AI)-based optimization layer for adaptive decision-making. A Petri Net supervisory control mechanism is introduced to manage signal transitions and enable emergency vehicle pre-emption. These results were obtained through MATLAB-SUMO co-simulation across multiple traffic scenarios. Results demonstrate significant improvements, including reduced queue length and delay, increased throughput, and enhanced congestion management compared to conventional methods. The proposed model provides a scalable and intelligent solution for modern smart city traffic systems.

The Collaborative Green Vehicle Routing Problem with Time-Dependent Travel Speeds

This study investigates the collaborative green vehicle routing problem with time-dependent travel speeds (CGVRP-TD), which integrates horizontal collaboration among multiple depots with time-dependent traffic conditions. The problem jointly optimizes customer allocation, vehicle routing, and departure-time decisions to minimize transportation-related carbon emissions subject to vehicle capacity and customer time-window constraints. We formulate the CGVRP-TD as a mixed-integer programming model and develop a two-phase adaptive large neighborhood search algorithm with embedded departure-time optimization. The first phase explores routing and customer-assignment decisions using problem-specific operators, including two speed-related removal operators, while the second phase applies exact departure-time optimization to fixed routes. Computational experiments show that the proposed algorithm obtains high-quality solutions efficiently and that both departure-time optimization and speed-related operators contribute to emission reduction. The results further demonstrate that combining horizontal collaboration with time-dependent travel-speed information can substantially reduce transportation emissions while preserving on-time service. We also discuss emission-savings allocation mechanisms for sustaining collaboration among participating depots.

Travel Behavior and Congestion Tolling Strategies in a Bi-Modal Bottleneck Model with Autonomous and Human-Driven Vehicles under Linear Scheduling Preferences

In recent years, activity-based bottleneck models have been widely used to address time allocation between commuting and activities. However, most previous studies adopted constant utility preferences and overlooked the dynamic marginal utility of time. This paper introduces a linear utility preference, assuming that marginal utility changes linearly over time, and recognizes that in-vehicle activities generally yield lower marginal utility than activities at home or at work because of limited physical resources, interpersonal interaction, and comfort. We examine bottleneck congestion in a bi-modal system with autonomous and human-driven vehicles, and analyze commuters’ travel time choices during the morning peak equilibrium. We then investigate congestion pricing and propose two schemes: a time-varying toll and a step toll. The results show that scheduling preferences significantly affect travel patterns and pricing strategies. The total social cost under linear scheduling preferences is substantially lower than that under constant scheduling preferences, suggesting that models with constant scheduling preferences may overestimate social cost.

A Decentralized Traffic Signal Control Framework Using Multiagent Reinforcement Learning With Real-World Operational Constraints