arXiv subjects

Gustav Nilsson

Publications and source records attributed to Gustav Nilsson.

At least 19 recordsLinked to original sources

arXiv2026

A Convex Formulation of the Multi-Commodity Dynamic Traffic Assignment

We consider a multi-commodity Dynamic Traffic Assignment (DTA) problem formulated as a network flow control problem on the Cell Transmission Model (CTM). The objective is to design optimal control policies using variable speed limits, ramp metering, and dynamic routing to regulate traffic evolution over time on a given limited-capacity transportation network. Even simple instances of DTA problems on the CTM are known to give rise to non-convex optimal control formulations. Nevertheless, a single-commodity DTA formulation has recently been proposed that admits a tight convex relaxation, thereby enabling tractable optimal control synthesis. The single-commodity formulation, however, is structurally restrictive, as it effectively allows only a single destination. To address this limitation, we develop a multi-commodity CTM model in which each commodity is associated with potentially distinct sets of off-ramps. By extending the convexification approach developed for the single-commodity case, we establish a tight convex relaxation of the multi-commodity DTA problem on the CTM model. This relaxation relies on concave, commodity-specific demand functions and concave aggregate supply functions for every cell, which ensure convexity of the resulting optimal control problem. Our proposed formulation requires commodity-dependent implementation of variable speed limits and dynamic routing policies.

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arXiv2025

On Convexity of Optimal Multi-Commodity Freeway Network Control

We study a multi-commodity Freeway Network Control (FNC) problem aiming at achieving optimal operation of a transportation network through the use of ramp metering and variable speed limits. Straightforward formulations of both single- and multi-commodity FNC problems based on the Cell Transmission Model are known to be non-convex, mainly due to the congestion effects at diverge junctions. However, recent studies have shown that it is possible to formulate a tight convex relaxation of the single-commodity FNC problem. We extend these results to the multi-commodity FNC problem by considering concave commodity-specific demand functions and concave aggregate supply functions, so that different variable speed limits can be applied to different commodities. Hence, it is possible to efficiently compute the optimal control action to reduce congestion phenomena in the network. We also present a case study of a segment of the freeway network in California, using data from the PeMS database, to demonstrate the effectiveness of the proposed solution. Finally, we draw a comparison with a setting where the multi-commodity flows are modeled and controlled as a single-commodity flow, to emphasize the relevance of acting separately on different classes of vehicles.

math.OC↗

arXiv2025

Resource-Splitting Games with Tullock-Based Lossy Contests

This paper introduces a novel class of multi-stage resource allocation games that model real-world scenarios in which profitability depends on the balance between supply and demand, and where higher resource investment leads to greater returns. Our proposed framework, which incorporates the notion of profit loss due to insufficient player participation, gives rise to a Tullock-like functional form of the stage payoff structure when weighted fair proportional resource allocation is applied. We explore both centralized and Nash equilibrium strategies, establish sufficient conditions for their existence and uniqueness, and provide an iterative, semi-decentralized method to compute the Nash equilibrium in games with arbitrarily many players. Additionally, we demonstrate that the framework generalizes instances of several existing models, including Receding Horizon and Blotto games, and present a semi-analytical method for computing the unique Nash equilibrium within the Blotto setup. Our findings are validated through a numerical case study in smart mobility, highlighting the practical relevance and applicability of the proposed model.

cs.GT↗

arXiv2025

Gravitational instantons with $S^1$ symmetry

Uniqueness results for asymptotically locally flat and asymptotically flat $S^1$-symmetric gravitational instantons are proved using a divergence identity of the type used in uniqueness proofs for static black holes, combined with results derived from the $G$-signature theorem. Our results include a proof of the $S^1$-symmetric version of the Euclidean Black Hole Uniqueness conjecture, a uniqueness result for the Taub-bolt family of instantons, as well as a proof that an ALF $S^1$-symmetric instanton with the topology of the Chen-Teo family of instantons is Hermitian.

math.DG↗

arXiv2024

Receding-Horizon Games with Tullock-Based Profit Functions for Electric Ride-Hailing Markets

This paper proposes a receding-horizon, game-theoretic charging planning mechanism for electric ride-hailing markets. As the demand for ride-hailing services continues to surge and governments advocate for stricter environmental regulations, integrating electric vehicles into these markets becomes inevitable. The proposed framework addresses the challenges posed by dynamic demand patterns, fluctuating energy costs, and competitive dynamics inherent in such markets. Leveraging the concept of receding-horizon games, we propose a method to optimize proactive dispatching of vehicles for recharging over a predefined time horizon. We integrate a modified Tullock contest that accounts for customer abandonment due to long waiting times to model the expected market share, and by factoring in the demand-based electricity charging, we construct a game capturing interactions between two companies over the time horizon. For this game, we first establish the existence and uniqueness of the Nash equilibrium and then present a semi-decentralized, iterative method to compute it. Finally, the method is evaluated in an open-loop and a closed-loop manner in a simulated numerical case study.

eess.SY↗

arXiv2024

Topology of Toric Gravitational Instantons

For an asymptotically locally Euclidean (ALE) or asymptotically locally flat (ALF) gravitational instanton $(M,g)$ with toric symmetry, we express the signature of $(M,g)$ directly in terms of its rod structure. Applying Hitchin$\unicode{x2013}$Thorpe-type inequalities for Ricci-flat ALE/ALF manifolds, we formulate, as a step toward a classification of toric ALE/ALF instantons, necessary conditions that the rod structures of such spaces must satisfy. Finally, we apply these results to the study of rod structures with three turning points.

math.DG↗

arXiv2024

Mode Stability for Gravitational Instantons of Type D

We study Ricci-flat perturbations of gravitational instantons of Petrov type D. Analogously to the Lorentzian case, the Weyl curvature scalars of extreme spin-weight satisfy a Riemannian version of the separable Teukolsky equation. As a step towards rigidity of the type D Kerr and Taub-bolt families of instantons, we prove mode stability, i.e., that the Teukolsky equation admits no solutions compatible with regularity and asymptotic (local) flatness.

math.DG↗

arXiv2024

A Blotto Game Approach to Ride-hailing Markets with Electric Vehicles

When a centrally operated ride-hailing company considers to enter a market already served by another company, it has to make a strategic decision about how to distribute its fleet among different regions in the area. This decision will be influenced by the market share the company can secure and the costs associated with charging the vehicles in each region, all while competing with the company already operating in the area. In this paper, we propose a Colonel Blotto-like game to model this decision-making. For the class of games that we study, we first prove the existence and uniqueness of a Nash Equilibrium. Subsequently, we provide its general characterization and present an algorithm for computing the ones in the feasible set's interior. Additionally, for a simplified scenario involving two regions, which would correspond to a city area with a downtown and a suburban region, we also provide a method to check for the equilibria on the feasible set's boundary. Finally, through a numerical case study, we illustrate the impact of charging prices on the position of the Nash equilibrium.

eess.SY↗

arXiv2024

Macroscopic pricing schemes for the utilization of pool ride-hailing vehicles in bus lanes

With the increasing popularity of ride-hailing services, new modes of transportation are having a significant impact on the overall performance of transportation networks. As a result, there is a need to ensure that both the various transportation alternatives and the spatial network resources are used efficiently. In this work, we analyze a network configuration where part of the urban transportation network is devoted to dedicated bus lanes. Apart from buses, we let pool ride-hailing trips use the dedicated bus lanes which, contingent upon the demand for the remaining modes, may result in faster trips for users opting for the pooling alternative. Under an aggregated modelling framework, we characterize the spatial configuration and the multi-modal demand split for which this strategy achieves a system optimum. For these specific scenarios, we compute the equilibrium when ride-hailing users can choose between solo and pool services, and we provide a pricing scheme for mitigating the gap between total user delays of the system optimum and user equilibrium solutions, when needed.

eess.SY↗

arXiv2024

On decentralized computation of the leader's strategy in bi-level games

Motivated by the omnipresence of hierarchical structures in many real-world applications, this study delves into the intricate realm of bi-level games, with a specific focus on exploring local Stackelberg equilibria as a solution concept. While existing literature offers various methods tailored to specific game structures featuring one leader and multiple followers, a comprehensive framework providing formal convergence guarantees to a local Stackelberg equilibrium appears to be lacking. Drawing inspiration from sensitivity results for nonlinear programs and guided by the imperative to maintain scalability and preserve agent privacy, we propose a decentralized approach based on the projected gradient descent with the Armijo stepsize rule. The main challenge here lies in assuring the existence and well-posedness of Jacobians that describe the leader's decision's influence on the achieved equilibrium of the followers. By meticulous tracking of the Implicit Function Theorem requirements at each iteration, we establish formal convergence guarantees to a local Stackelberg equilibrium for a broad class of bi-level games. Building on our prior work on quadratic aggregative Stackelberg games, we also introduce a decentralized warm-start procedure based on the consensus alternating direction method of multipliers addressing the previously reported initialization issues. Finally, we provide empirical validation through two case studies in smart mobility, showcasing the effectiveness of our general method in handling general convex constraints, and the effectiveness of its extension in tackling initialization issues.

eess.SY↗

arXiv2023

A Dynamic Macroscopic Framework for Pricing of Ride-hailing Services with an Optional Bus Lane Access for Pool Vehicles

On-demand trip sharing is an efficient solution to mitigate the negative impact e-hailing has on congestion. It motivates platform operators to reduce their fleet size, and serves the same demand level with a lower effective distance traveled. Users nevertheless prefer to travel solo and for shorter distances despite the fare discount they receive. By offering them the choice to pool and travel in high occupancy dedicated bus lanes, we provide them with a larger incentive to share their rides, yet this creates additional bus delays. In this work, we develop dynamic feedback-based control schemes that adjust the price gap between solo and pool trips to improve multi-modal delays. First, we develop a modal- and space-dependent aggregate model for private vehicles, ride-pooling, and buses, and we use this model to test different control strategies. To minimize the error between the target and actual speeds in the bus network, we design a PI controller and show that by adjusting pool trip fares, we can, with little input data, minimize this error. We also put forward a Model Predictive Control (MPC) framework to minimize the total Passenger Hours Traveled (PHT) and Waiting Times (WT) for the different travelers. Moreover, we show how the MPC framework can be utilized to impose a minimum speed in dedicated bus lanes to ensure that the buses operate on schedule. The results mark the possibility of improving the overall network conditions by incentivizing or discouraging pooling in the vehicle or bus network.

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arXiv2023

Learning How to Price Charging in Electric Ride-Hailing Markets

With the electrification of ride-hailing fleets, there will be a need to incentivize where and when the ride-hailing vehicles should charge. In this work, we assume that a central authority wants to control the distribution of the vehicles and can do so by selecting charging prices. Since there will likely be more than one ride-hailing company in the market, we model the problem as a single-leader multiple-follower Stackelberg game. The followers, i.e., the companies, compete about the charging resources under given prices provided by the leader. We present a learning algorithm based on the concept of contextual bandits that allows the central authority to find an efficient pricing strategy. We also show how the exploratory phase of the learning can be improved if the leader has some partial knowledge about the companies' objective functions. The efficiency of the proposed algorithm is demonstrated in a simulated case study for the city of Shenzhen, China.

eess.SY↗

arXiv2023

GreenEVT: Greensboro Electric Vehicle Testbed

The ongoing electrification of the transportation fleet will increase the load on the electric power grid. Since both the transportation network and the power grid already experience periods of significant stress, joint analyses of both infrastructures will most likely be necessary to ensure acceptable operation in the future. To enable such analyses, this paper presents an open-source testbed that jointly simulates high-fidelity models of both the electric distribution system and the transportation network. The testbed utilizes two open-source simulators, OpenDSS to simulate the electric distribution system and the microscopic traffic simulator SUMO to simulate the traffic dynamics. Electric vehicle charging links the electric distribution system and the transportation network models at vehicle locations determined using publicly available parcel data. Leveraging high-fidelity synthetic electric distribution system data from the SMART-DS project and transportation system data from OpenStreetMap, this testbed models the city of Greensboro, NC down to the household level. Moreover, the methodology and the supporting scripts released with the testbed allow adaption to other areas where high-fidelity geolocated OpenDSS datasets are available. After describing the components and usage of the testbed, we exemplify applications enabled by the testbed via two scenarios modeling the extreme stresses encountered during evacuations.

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arXiv2023

On Finding the Leader's Strategy in Quadratic Aggregative Stackelberg Pricing Games

This paper analyzes a class of Stackelberg games where different actors compete for shared resources and a central authority tries to balance the demand through a pricing mechanism. Situations like this can for instance occur when fleet owners of electric taxi services compete about charging spots. In this paper, we model the competition between the followers as an aggregative game, i.e., each player's decision only depends on the aggregate strategy of the others. While it has previously been shown that there exist dynamic pricing strategies to achieve the central authority's objective, we in this paper present a method to compute optimal static prices. Proof of convergence of the method is presented, together with a numerical study showcasing the benefits and the speed of convergence of the proposed method.

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arXiv2022

Hierarchical Pricing Game for Balancing the Charging of Ride-Hailing Electric Fleets

Due to the ever-increasing popularity of ride-hailing services and the indisputable shift towards alternative fuel vehicles, the intersection of the ride-hailing market and smart electric mobility provides an opportunity to trade different services to achieve societal optimum. In this work, we present a hierarchical, game-based, control mechanism for balancing the simultaneous charging of multiple ride-hailing fleets. The mechanism takes into account sometimes conflicting interests of the ride-hailing drivers, the ride-hailing company management, and the external agents such as power-providing companies or city governments that will play a significant role in charging management in the future. The upper-level control considers charging price incentives and models the interactions between the external agents and ride-hailing companies as a Reverse Stackelberg game with a single leader and multiple followers. The lower-level control motivates the revenue-maximizing drivers to follow the company operator's requests through surge pricing and models the interactions as a single leader, multiple followers Stackelberg game. We provide a pricing mechanism that ensures the existence of a unique Nash equilibrium of the upper-level game that minimizes the external agent's objective at the same time. We provide theoretical and experimental robustness analysis of the upper-level control with respect to parameters whose values depend on sensitive information that might not be entirely accessible to the external agent. For the lower-level algorithm, we combine the Nash equilibrium of the upper-level game with a quadratic mixed integer optimization problem to find the optimal surge prices. Finally, we illustrate the performance of the control mechanism in a case study based on real taxi data from the city of Shenzhen in China.

eess.SY↗

arXiv2022

Safe Schedule Verification for Urban Air Mobility Networks with Node Closures

In Urban Air Mobility (UAM) networks, takeoff and landing sites, called vertiports, are likely to experience intermittent closures due to, e.g., adverse weather. To ensure safety, all in-flight Urban Air Vehicles (UAVs) in a UAM network must therefore have alternative landing sites with sufficient landing capacity in the event of a vertiport closure. In this paper, we study the problem of safety verification of UAM schedules in the face of vertiport closures. We first provide necessary and sufficient conditions for a given UAM schedule to be safe in the sense that, if a vertiport closure occurs, then all UAVs will be able to safely land at a backup landing site. Next, we convert these conditions to an efficient algorithm for verifying safety of a UAM schedule via a linear program by using properties of totally unimodular matrices. Our algorithm allows for uncertain travel time between UAM vertiports and scales quadratically with the number of scheduled UAVs. We demonstrate our algorithm on a UAM network with up to 1,000 UAVs.

eess.SY↗

arXiv2022

A Pricing Mechanism for Balancing the Charging of Ride-Hailing Electric Vehicle Fleets

Both ride-hailing services and electric vehicles are becoming increasingly popular and it is likely that charging management of the ride-hailing vehicles will be a significant part of the ride-hailing company's operation in the near future. Motivated by this, we propose a game theoretic model for charging management, where we assume that it is the fleet-operator that wants to minimize its operational cost, which among others include the price of charging. To avoid overcrowded charging stations, a central authority will design pricing policies to incentivize the vehicles to spread out among the charging stations, in a setting where several ride-hailing companies compete about the resources. We show that it is possible to construct pricing policies that make the Nash-equilibrium between the companies follow the central authority's target value when the desired load is feasible. Moreover, we provide a decentralized algorithm for computation of the equilibrium and conclude the paper with a numerical example illustrating the results.

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arXiv2021

Sensitivity to User Mischaracterizations in Electric Vehicle Charging

In this paper, we consider electric vehicle charging facilities that offer various levels of service for varying prices such that rational users choose a level of service that minimizes the total cost to themselves including an opportunity cost that incorporates users' value of time. In this setting, we study the sensitivity of the expected occupancy at the facility to mischaracterizations of user profiles and uncharacterized heterogeneity. For user profile mischaracterizations, we first provide a fundamental upper bound for the difference between the expected occupancy under any two different distributions on a user's impatience (i.e., value of time) that only depends on the minimum and maximum charging rate offered by the charging facility. Next, we consider the case when a user's impatience is a discrete random variable and study the sensitivity of the expected occupancy to the probability masses and attained values of the random variable. We show that the expected occupancy varies linearly with respect to the probability masses and is piecewise constant with respect to the attained values. Furthermore, we study the effects on the expected occupancy from the occurrence of heterogeneous user populations. In particular, we quantify the effect on the expected occupancy from the existence of sub-populations that may only select a subset of the offered service levels. Lastly, we quantify the variability of early departures on the expected occupancy. These results demonstrate how the facility operator might design prices such that the expected occupancy does not vary much under small changes in the distribution of a user's impatience, variable and limited user service needs, or uncharacterized early departure, quantities which are generally difficult to characterize accurately from data. We further demonstrate our results via examples.

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