About Me
Hi! I’m Michael, a PhD student at the University of Passau in algorithmic game theory under the supervision of Prof. Dr. Tobias Harks. I study various variants of traffic assignment problems with a game theoretical perspective. I am particularly interested in analyzing dynamic models, i.e., models that capture the interaction of traffic flow at different times of a day, as well as multi-modal traffic infrastructure.
Publications
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Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle CapacitiesJun, 2024. Joint work with Tobias Harks, Sven Jäger, and Philine Schiewe.Abstract: Modelling passenger assignments in public transport networks is a fundamental task for city planners, especially when deliberating network infrastructure decisions. A key aspect of a realistic model for passenger assignments is to integrate selfish routing behaviour of passengers on the one hand, and the limited vehicle capacities on the other hand. We formulate a side-constrained user equilibrium model in a schedule-based time-expanded transit network, where passengers are modelled via a continuum of non-atomic agents that want to travel with a fixed start time from a user-specific origin to a destination. An agent’s route may comprise several rides along given lines, each using vehicles with hard loading capacities. We give a characterization of (side-constrained) user equilibria via a quasi-variational inequality and prove their existence by generalizing a well-known existence result of Bernstein and Smith (Transp. Sci., 1994). We further derive a polynomial time algorithm for single-commodity instances and an exact finite time algorithm for the multi-commodity case. Based on our quasi-variational characterization, we finally devise a fast heuristic computing user equilibria, which is tested on real-world instances based on data gained from the Hamburg S-Bahn system and the Swiss long-distance train network. It turns out that w.r.t. the total travel time, the computed user-equilibria are quite efficient compared to a system optimum, which neglects equilibrium constraints and only minimizes total travel time.
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Machine-Learned Prediction Equilibrium for Dynamic Traffic AssignmentSep, 2021. Joint work with Lukas Graf, Tobias Harks, and Kostas Kollias.Abstract: We study a dynamic traffic assignment model, where agents base their instantaneous routing decisions on real-time delay predictions. We describe a general mathematical model which, in particular, includes the settings leading to IDE and DE. On the theoretical side we show existence of equilibrium solutions under some additional assumptions while on the practical side we implement a machine-learned predictor and compare it to other static predictors.
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A Process Algebra for Link Layer ProtocolsApr, 2019. Joint work with Rob van Glabbeek and Peter Höfner.Abstract: We propose a process algebra for link layer protocols, featuring a unique mechanism for modelling frame collisions. We also formalise suitable liveness properties for link layer protocols specified in this framework. To show applicability we model and analyse two versions of the Carrier-Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol. Our analysis confirms the hidden station problem for the version without virtual carrier sensing. However, we show that the version with virtual carrier sensing not only overcomes this problem, but also the exposed station problem with probability 1. Yet the protocol cannot guarantee packet delivery, not even with probability 1.
Blog Posts
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Kubuntu CustomizationsJul 16, 2021: A collection of my Kubuntu and KDE customizations to get the best working experience. These are only based on my personal preference.
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First PostJan 28, 2021: This is my first post on my personal blog based on Hugo.