A model for a network of conveyor belts with discontinuous speed and capacity

TL;DR

This paper presents a macroscopic model for conveyor belt networks with varying speeds and capacities, using scalar conservation laws with discontinuous flux to describe the dynamics and coupling conditions at intersections.

Contribution

It introduces a novel model for conveyor belt networks incorporating discontinuous flux functions and provides a well-posed solution framework with numerical validation.

Findings

Model accurately captures conveyor belt dynamics with capacity constraints

Coupling conditions ensure well-posed solutions at intersections

Numerical simulations confirm theoretical predictions

Abstract

We introduce a macroscopic model for a network of conveyor belts with various speeds and capacities. In a different way from traffic flow models, the product densities are forced to move with a constant velocity unless they reach a maximal capacity and start to queue. This kind of dynamics is governed by scalar conservation laws consisting of a discontinuous flux function. We define appropriate coupling conditions to get well-posed solutions at intersections and provide a detailed description of the solution. Some numerical simulations are presented to illustrate and confirm the theoretical results for different network configurations.