PRONTO: Public TRansport Networks via StOchastic Partial DiffereNTial EquatiOns

Research Project, 2027 – 2028

Urban transport networks are inherently dynamic and uncertain: passenger demand fluctuates randomly, delays propagate through interconnected routes, and external disruptions such as weather or infrastructure failures and road constructions infers persistent complexity. Traditional modeling approaches—such as discrete-event simulation or queueing models—often treat uncertainty through repeated simulations rather than incorporating randomness directly into the governing transport network dynamics. But, why so? It is because, we believe, systematic modeling framework at scale does not exist, denying networkwide curing of eventual public transport service sensitivity analysis, interruptions, re-configuration. This project proposes a novel framework: stochastic partial differential equations (SPDEs) across modalities and emulate passenger flows.

The proposed research treats public transport as a spatially distributed stochastic system. Passenger densities, vehicle flows, and delay propagation are modeled as continuous fields in space and time under random perturbations. SPDEs provide a mathematical home to capture both deterministic transport mechanisms (e.g., flow, diffusion, network connectivity) and stochastic influences (e.g., demand shocks, incidents). For network-scale transport systems, graph-based SPDEs incorporate the topology of the existing infrastructure (e.g. tram lines) while modeling delay and density evolution under uncertainty is described by the randomness in the SPDEs.

The major expected outcome is a new analytical and computational toolkit for resilience assessment, strategic planning (e.g. automation, infrastructure rebuilds) and delay minimal reconfiguration solutions. The approach is interdisciplinary, combining applied mathematics, transport and system engineering, and data science. It offers a novel perspective on understanding and managing uncertainty in large-scale infrastructure systems. PRONTO!