arXiv subjects

Thomas Kjær Rasmussen

Publications and source records attributed to Thomas Kjær Rasmussen.

10 recordsLinked to original sources

arXiv2026

Sensitivity analysis of the perturbed utility stochastic traffic equilibrium

This paper develops a sensitivity analysis framework for the perturbed utility route choice (PURC) model and the accompanying stochastic traffic equilibrium model. We derive analytical sensitivity expressions for the Jacobian of the individual optimal PURC flow and equilibrium link flows with respect to link cost parameters under general assumptions. This allows us to determine the marginal change in link flows following a marginal change in link costs across the network. We show how to implement these results while exploiting the sparsity generated by the PURC model. Numerical examples illustrate the use of our method for estimating equilibrium link flows after link cost shifts, identifying critical design parameters, and quantifying uncertainty in performance predictions. Finally, we demonstrate the method in a large-scale example. The findings have implications for network design, pricing strategies, and policy analysis in transportation planning and economics, providing a bridge between theoretical models and real-world applications.

econ.EM↗

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↗

arXiv2023

Perturbed utility stochastic traffic assignment

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We formulate the PURC equilibrium assignment problem as a convex minimization problem and find a closed-form stochastic network loading expression that allows us to formulate the Lagrangian dual of the assignment problem as an unconstrained optimization problem. To solve this dual problem, we formulate a quasi-Newton accelerated gradient descent algorithm (qN-AGD*). Our numerical evidence shows that qN-AGD* clearly outperforms a conventional primal algorithm as well as a plain accelerated gradient descent algorithm. qN-AGD* is fast with a runtime that scales about linearly with the problem size, indicating that solving the perturbed utility assignment problem is feasible also with very large networks.

math.OC↗

arXiv2022

Bikeability and the induced demand for cycling

To what extent is the volume of urban bicycle traffic affected by the provision of bicycle infrastructure? In this study, we exploit a large dataset of observed bicycle trajectories in combination with a fine-grained representation of the Copenhagen bicycle-relevant network. We apply a novel model for bicyclists' choice of route from origin to destination that takes the complete network into account. This enables us to determine bicyclists' preferences for a range of infrastructure and land-use types. We use the estimated preferences to compute a subjective cost of bicycle travel, which we correlate with the number of bicycle trips across a large number of origin-destination pairs. Simulations suggest that the extensive Copenhagen bicycle lane network has caused the number of bicycle trips and the bicycle kilometers traveled to increase by 60% and 90%, respectively, compared with a counterfactual without the bicycle lane network. This translates into an annual benefit of EUR 0.4M per km of bicycle lane owing to changes in subjective travel cost, health, and accidents. Our results thus strongly support the provision of bicycle infrastructure.

econ.EM↗

arXiv2021

A perturbed utility route choice model

We propose a route choice model in which traveler behavior is represented as a utility maximizing assignment of flow across an entire network under a flow conservation constraint}. Substitution between routes depends on how much they overlap. {\tr The model is estimated considering the full set of route alternatives, and no choice set generation is required. Nevertheless, estimation requires only linear regression and is very fast. Predictions from the model can be computed using convex optimization, and computation is straightforward even for large networks. We estimate and validate the model using a large dataset comprising 1,337,096 GPS traces of trips in the Greater Copenhagen road network.

econ.EM↗