arXiv subjects

Otto Anker Nielsen

Publications and source records attributed to Otto Anker Nielsen.

8 recordsLinked to original sources

arXiv2026

An ALNS Heuristic for Large-Scale Line Planning with Mode Choice and Line Generation

Demand responsiveness is an important consideration in public transport line planning, as network design and service quality influence passenger demand. However, accounting for this interaction further complicates an already challenging combinatorial optimization problem. To address this challenge, we propose a scalable Adaptive Large Neighborhood Search (ALNS) algorithm for large-scale line planning with endogenous demand. The algorithm jointly optimizes lines and frequencies while accounting for passenger mode choice, passenger assignment, and vehicle capacities. Candidate lines are generated dynamically throughout the search, and solutions are evaluated using an embedded evaluation procedure for passenger assignment and demand estimation, together with a dedicated local search procedure for frequency optimization. The proposed methodology is evaluated on the public transport network of Odense, Denmark, comprising approximately 1,800 origin-destination pairs. Computational results demonstrate the applicability of the approach to realistic, large-scale instances. The optimized networks concentrate resources on fewer, higher-frequency services, reducing average headways from approximately 41 minutes to 6.8-13 minutes while substantially increasing public transport ridership. Furthermore, the results show that network design is highly sensitive to assumptions regarding passenger behavior, highlighting the importance of carefully calibrated demand models when incorporating demand responsiveness into line planning.

math.OC↗

arXiv2026

An Exact Algorithm for Public Transport Line Planning Considering Passenger and Operational Costs and Lost Demand

Line planning in public transport is the strategic problem of selecting lines and their operating frequencies. This problem is important as it defines the passenger service, based on available connections and expected travel times, and drives operational cost in terms of the number of vehicles required. This paper presents a line planning model that minimizes the weighted sum of passenger travel time, including in-vehicle time and frequency-dependent waiting and transfer times, and operating costs for the public transport agency. Unlike traditional approaches that assume demand to be fixed, our approach requires a minimum service level for demand to be captured, ensuring that services are provided only when they are attractive to users and cost-efficient to operate. The introduced capacity constraints ensure sufficient capacity on the lines and help guide the trade-off between expected demand on selected lines and their frequencies. The resulting mixed-integer program presents a challenging combinatorial problem as the number of passenger paths grows rapidly in relation to the number of lines and frequencies considered. To address this, we propose an iterative exact algorithm that utilizes a reduced problem representation and dynamically expands it with additional frequencies and paths. Evaluated on four networks with varying complexity and cost trade-offs, our method achieves significant speed-ups and tighter bounds compared to solving the complete model directly by CPLEX, particularly when operator and passenger costs are more evenly balanced in the objective. Furthermore, we demonstrate how accounting for lost demand leads to more efficient resource use from an overall perspective.

math.OC↗

arXiv2025

Safe and Operationally Efficient Longitudinal Control of Autonomous Truck Platoons

This paper presents a hierarchical longitudinal control architecture for autonomous truck platoons that jointly addresses safety, string stability, and economic efficiency. The framework integrates a high-rate safety projection filter, a spacing-regulation layer based on a lag-aware proportional-integral-derivative (PID) controller, and a slow-timescale economic optimizer balancing fuel consumption and travel time. The safety layer guarantees collision avoidance under bounded actuation delays by enforcing forward invariance of a velocity-aware headway constraint through a high-order control barrier function. The regulation layer shapes the spacing-error dynamics into a second-order form with interpretable parameters for damping and natural frequency while explicitly accounting for actuator lag. At the macroscopic level, fuel use is modeled by a tractive-power relation that captures aerodynamic benefits of close spacing, enabling a long-term optimization of speed trajectories subject to comfort and energy trade-offs. We show that the closed-loop dynamics converge to the Optimal Velocity Model with Relative Velocity (OVRV) under undisturbed conditions and derive worst-case upper bounds for platoon stabilization time. Numerical case studies demonstrate the superiority of the proposed design over an canonical baseline controllers in both transient behavior and long-term energy efficiency.

math.OC↗

arXiv2025

Improving Travel Time Reliability with Variable Speed Limits

This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is a linear combination of the expected value and standard deviation of average travel time, with traffic flow dynamics following the kinematic wave model (Lighthill, 1955; Richards, 1956). We develop two complementary models to optimally set variable speed limits: In the first model, daily peak traffic demand is conceptualized as a stochastic variable, and the resulting model is solved through a three-stage optimization algorithm. The second model is based on deterministic demand, instead modeling bottleneck capacity as a stochastic process using a stochastic differential equation (SDE). The practical applicability of both approaches is demonstrated through numerical examples with empirically calibrated data.

math.OC↗

arXiv2025

Travel Time Reliability in Stochastic Kinematic Flow Models

This paper analyzes the time-dependent relationship between the mean and variance of travel time on a single corridor under rush hour like congestion patterns. To model this phenomenon, we apply the LWR ((Lighthill & Whitham, 1955), (Richards, 1956)) theory on a homogenous freeway with a discontinuous bottleneck at its downstream end, assuming a uni-modal demand profile with a stochastic peak. We establish conditions for typical counterclockwise hysteresis loops under these assumptions. It is demonstrated that shapes of the fundamental diagram which always produce a counterclockwise loop can be interpreted as an indication of aggressive driving behavior, while deviations may occur under defensive driving. This classification enables a detailed explanation of the qualitative physical mechanisms behind this pattern, as well as an analysis of the causes for quantitatively limited deviations. Some of the mathematical properties of the LWR model identified in our analysis have not yet been addressed in the literature and we critically examine the extent to which these reflect actual traffic flow behavior. Our considerations are supported by numerical experiments. The obtained results aim to improve the fundamental understanding of the physical causes of this hysteresis pattern and to facilitate its better estimation in traffic planning and control.

physics.soc-ph↗

arXiv2025

Risk Aware Reservoir Control For Safer Urban Traffic Networks

We present a risk-aware perimeter-style controller that couples safety and efficiency targets in large, heterogeneous urban traffic networks. The network is compressed into two interacting "reservoirs" whose dynamics follow the Generalized Bathtub Model, while accidents are described by a self-exciting (Hawkes) counting process whose intensity depends on vehicle exposure, speed dispersion between reservoirs and accident clustering. Accident occurrences feed back into operations through an analytically simple degradation factor that lowers speed and discharge capacity in proportion to the live accident load. A receding-horizon policy minimizes a mixed delay-safety objective that includes a variance penalty capturing risk aversion; the resulting open-loop problem is shown to possess a bang-bang optimum whose gates switch only at accident times. This structure enables an event-triggered MPC that only re-optimizes when new accidents occur, reducing on-line computation significantly. Parameters are calibrated using OpenStreetMap data for metropolitan Copenhagen to analyze traffic dynamics during morning peak commuter demand. Monte-Carlo simulations demonstrate delay savings of up to 30% and accident reductions of up to 35% relative to an uncontrolled baseline, with a transparent trade-off governed by a single risk parameter.

math.OC↗

arXiv2025

Using Model Predictive Control To Reduce Traffic Emissions on Urban Freeways

Urban traffic congestion significantly impacts regional air quality and contributes substantially to pollutant emissions. Suburban freeway corridors are a major source of traffic-related emissions, particularly nitrogen oxides (NOx) and carbon dioxide (CO2). This paper proposes a Model Predictive Control (MPC) framework aimed at emission reduction on peripheral freeway corridors. Emission rates on freeways exhibit high sensitivity to speed fluctuations and congestion recovery processes. To address this relationship, we develop and analyze a bounded-acceleration continuum traffic flow model. By introducing an upper limit on vehicle acceleration capabilities, we enhance behavioral realism through the incorporation of driver responses to congestion, which is widely recognized as a main cause of the important capacity drop phenomenon. Our approach implements dynamically optimized variable speed limits (VSLs) at strategic corridor locations, balancing the dual objectives of minimizing both travel time and emissions as quantified by the COPERT V [1] model. Numerical simulations demonstrate that this framework effectively manages congestion and reduces emissions across various traffic demand scenarios.

math.OC↗

arXiv2024

Hysteresis Behind A Freeway Bottleneck With Location-Dependent Capacity

Macroscopic fundamental diagrams (MFDs) and related network traffic dynamics models have received both theoretical support and empirical validation with the emergence of new data collection technologies. However, the existence of well-defined MFD curves can only be expected for traffic networks with specific topologies and is subject to various disturbances, most importantly hysteresis phenomena. This study aims to improve the understanding of hysteresis in Macroscopic Fundamental Diagrams and Network Exit Functions (NEFs) during rush hour conditions. We apply the LWR theory to a highway corridor featuring a location-dependent downstream bottleneck to identify a figure-eight hysteresis pattern, clockwise on the top and counter-clockwise on the bottom. Our empirical observations confirm the occurrence of counter-clockwise loops in real conditions, an effect which we can attribute to demand asymmetries through theoretical analysis. The paper discusses the impact of the road topology and demand patterns on the formation and intensity of hysteresis loops analytically. To substantiate these findings, we analyze empirical MFD data from two bottlenecks and present statistical evidence that, under otherwise identical conditions, a continuous bottleneck causes less hysteresis than a discontinuous one. We conduct numerical experiments using the Cell Transmission Model (CTM) to show that even a slight reduction in the capacity of the homogeneous section can significantly decrease MFD hysteresis while maintaining outflow at the corridor's downstream end. These reductions can be achieved with minimal intervention through standard traffic control measures, such as dynamic speed limits or ramp metering.

cond-mat.stat-mech↗