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Mads Paulsen

Publications and source records attributed to Mads Paulsen.

5 recordsLinked to original sources

Robust design of bicycle infrastructure networks

Promoting active mobility like cycling relies on the availability of well-connected, high-quality bicycle networks. However, expanding these networks over an extended planning horizon presents one of the most complex challenges in transport science. This complexity arises from the intricate interactions between infrastructure availability and usage, such as network spillover effects and mode choice substitutions. In this paper, we approach the problem from two perspectives: direct optimization methods, which generate near-optimal solutions using operations research techniques, and conceptual heuristics, which offer intuitive and scalable algorithms grounded in network science. Specifically, we compare direct welfare optimization with an inverse network percolation approach to planning cycle superhighway extensions in Copenhagen. Interestingly, while the more complex optimization models yield better overall welfare results, the improvements over simpler methods are small. More importantly, we demonstrate that the increased complexity of planning approaches generally makes them more vulnerable to input uncertainty, reflecting the bias-variance tradeoff. This issue is particularly relevant in the context of long-term planning, where conditions change during the implementation of the planned infrastructure expansions. Therefore, while planning bicycle infrastructure is important and renders exceptionally high benefit-cost ratios, considerations of robustness and ease of implementation may justify the use of more straightforward network-based methods.

physics.soc-ph

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

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

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

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