Control Strategies for Transport Networks under Demand Uncertainty

TL;DR

This paper develops control strategies for transport networks with uncertain demands modeled by stochastic differential equations, providing explicit control solutions and validating them through numerical simulations.

Contribution

It introduces a novel approach to controlling transport networks under demand uncertainty using linear hyperbolic PDEs and stochastic demand models, with explicit control calculations.

Findings

Explicit control strategies derived for uncertain demand scenarios

Numerical simulations confirm theoretical control effectiveness

Framework applicable to various demand assumptions

Abstract

In this article, we consider transport networks with uncertain demands. Network dynamics are given by linear hyperbolic partial differential equations and suitable coupling conditions, while demands are incorporated as solutions to stochastic differential equations. For the demand satisfaction, we solve a constrained optimal control problem. Controls in terms of network inputs are then calculated explicitly for different assumptions. Numerical simulations are performed to underline the theoretical results.