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arXiv · 2409.00619

On an Inverse Problem of the Generalized Bathtub Model of Network Trip Flows

Kuang Huang·Bangti Jin·Zhi Zhou
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Abstract

In this work, we investigate the generalized bathtub model, a nonlocal transport equation for describing network trip flows served by privately operated vehicles inside a road network. First, we establish the well-posedness of the mathematical model for both classical and weak solutions. Then we consider an inverse source problem of the model with model parameters embodying particular traffic situations. We establish a conditional Lipschitz stability of the inverse problem under suitable a priori regularity assumption on the problem data, using a Volterra integral formulation of the problem. Inspired by the analysis, we develop an easy-to-implement numerical method for reconstructing the flow rates, and provide the error analysis of the method. Further we present several numerical experiments to complement the theoretical analysis.

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Kuang Huang, Bangti Jin, Zhi Zhou. 2024-09-01. On an Inverse Problem of the Generalized Bathtub Model of Network Trip Flows. https://arxiv.org/abs/2409.00619

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