Towards a Statistical Physics of Collective Mobility and Demand-Driven Transport
by Andreas Sorge
Date of Examination:2017-06-19
Date of issue:2018-05-29
Advisor:Prof. Dr. Marc Timme
Referee:Prof. Dr. Marc Timme
Referee:Prof. Dr. Florentin Wörgötter
Persistent Address:
http://dx.doi.org/10.53846/goediss-6895
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Abstract
English
Collective mobility and demand-driven transport systems are vital to proper, efficient and sustainable functioning of biological, technical and social systems. They are relevant to mastering several major transitions human society is facing today on a global scale, and they have been attracting considerable interest as on-demand ride-sharing systems are projected to disrupt the individual mobility and public transport sector. In collective mobility systems and demand-driven transport systems alike, vehicles or other discrete mobile units carry individual passengers, goods or other discrete immobile loads. These systems do so upon individual request for transport from individual origins to individual destinations, within individual time windows. Coordination functions in these systems include assigning requests to transporters and routing the transporters within the underlying geometry. When transporters carry multiple loads at the same time, another function of the system is to bundle spatiotemporally overlapping requests. Given both the need and the recent interest and implementation of collective mobility and demand-driven transport systems, it is imperative to understand their core structural and dynamical properties and how they relate to their satisfactory and efficient functioning. Modelling and simulating such discrete-event systems involves untypical technicalities that presumably have hindered progress in studying these systems from the network dynamics and statistical physics perspective so far. In order to unlock collective mobility and demand-driven transport systems for studies in these fields, I devise a modular framework to model and simulate such systems. Furthermore, a fundamental steady-state performance measure is the transport capacity of the system. If overall demand exceeds capacity, the system congests and ceases to function. Determining the capacity is henceforth crucial to inform system design for optimized system efficiency and individual service quality. Intriguingly, the brink to congestion constitutes a critical transition reminiscent of percolation in time. I develop a dynamic notion of criticality of such stochastic processes, mapping the transition from stability to instabilty to a hybrid percolation phase transition. Overall, I anticipate this Thesis and the tools developed to be a starting point for modelling and studying the dynamics of collective mobility and demand-driven transport systems, and for understanding how the intricate interplay of their structure and their dynamics governs their functioning.
Keywords: demand-driven transport; statistical physics; python; collective mobility
