A model for a network of conveyor belts with discontinuous speed and capacity. (English) Zbl 1423.90077
Summary: 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.
MSC:
| 90B30 | Production models |
| 35L65 | Hyperbolic conservation laws |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
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