A Hyperbolic Transport Model for Passenger Flow on Tram Networks

TL;DR

This paper presents a hyperbolic PDE-based model for passenger flow in tram networks, incorporating stochastic boarding processes and uncertainty analysis to evaluate system robustness under delays and interruptions.

Contribution

It introduces a novel hyperbolic PDE framework coupled with stochastic processes for modeling urban tram passenger dynamics, including uncertainty quantification.

Findings

Model effectively captures passenger transport dynamics.

System robustness assessed under various uncertainties.

Framework adaptable to real-world tram network analysis.

Abstract

We introduce a modeling framework for an urban tram network based on a hyperbolic partial differential equation describing the transport of passengers along the network, coupled with a family of stochastic processes representing passenger boarding. Solutions are considered in a measure-valued sense. The system is further extended and subjected to uncertainties such as delays and service interruptions through a numerical study. Its robustness is assessed using appropriate risk measures.