On the Stability of Dynamical Multi-Commodity Flow Networks
(2025) 64th IEEE Conference on Decision and Control, CDC 2025 In Proceedings of the IEEE Conference on Decision and Control p.224-229- Abstract
We study a class of dynamical multi-commodity flows in transportation networks. These are modeled as dynamical systems describing the evolution of the densities of a number of different commodities across the cells of a transportation network. Each cell is characterized by commodity-specific increasing demand functions returning the maximum outflow of each commodity from the cell as a function of the current density of that commodity, as well as a decreasing supply function returning the total maximum inflow that is allowed in the cell as a function of the current aggregate density in the cell. Every commodity is characterized by a different routing matrix, whose entries describe the turning ratios between adjacent cells. We identify a... (More)
We study a class of dynamical multi-commodity flows in transportation networks. These are modeled as dynamical systems describing the evolution of the densities of a number of different commodities across the cells of a transportation network. Each cell is characterized by commodity-specific increasing demand functions returning the maximum outflow of each commodity from the cell as a function of the current density of that commodity, as well as a decreasing supply function returning the total maximum inflow that is allowed in the cell as a function of the current aggregate density in the cell. Every commodity is characterized by a different routing matrix, whose entries describe the turning ratios between adjacent cells. We identify a (typically convex) capacity region: for exogenous inflow vectors belonging to that region, we prove the existence of a locally asymptotically stable free-flow equilibrium point. Building on a contraction argument, we also provide an estimate of the basin of attraction of such free-flow equilibrium point. Finally, we analyze a simple special case showing that, when the exogenous inflow vector does not belong to the region of stability, non-free flow equilibrium points might arise.
(Less)
- author
- Sipione, Davide and Como, Giacomo LU
- organization
- publishing date
- 2025
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 2025 IEEE 64th Conference on Decision and Control, CDC 2025
- series title
- Proceedings of the IEEE Conference on Decision and Control
- pages
- 6 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 64th IEEE Conference on Decision and Control, CDC 2025
- conference location
- Rio de Janeiro, Brazil
- conference dates
- 2025-12-09 - 2025-12-12
- external identifiers
-
- scopus:105031900237
- ISSN
- 0743-1546
- 2576-2370
- ISBN
- 9798331526276
- DOI
- 10.1109/CDC57313.2025.11312216
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2025 IEEE.
- id
- f4ab0231-5c03-4bb1-b177-507aa47a7f8a
- date added to LUP
- 2026-05-04 13:03:19
- date last changed
- 2026-08-12 02:59:46
@inproceedings{f4ab0231-5c03-4bb1-b177-507aa47a7f8a,
abstract = {{<p>We study a class of dynamical multi-commodity flows in transportation networks. These are modeled as dynamical systems describing the evolution of the densities of a number of different commodities across the cells of a transportation network. Each cell is characterized by commodity-specific increasing demand functions returning the maximum outflow of each commodity from the cell as a function of the current density of that commodity, as well as a decreasing supply function returning the total maximum inflow that is allowed in the cell as a function of the current aggregate density in the cell. Every commodity is characterized by a different routing matrix, whose entries describe the turning ratios between adjacent cells. We identify a (typically convex) capacity region: for exogenous inflow vectors belonging to that region, we prove the existence of a locally asymptotically stable free-flow equilibrium point. Building on a contraction argument, we also provide an estimate of the basin of attraction of such free-flow equilibrium point. Finally, we analyze a simple special case showing that, when the exogenous inflow vector does not belong to the region of stability, non-free flow equilibrium points might arise.</p>}},
author = {{Sipione, Davide and Como, Giacomo}},
booktitle = {{2025 IEEE 64th Conference on Decision and Control, CDC 2025}},
isbn = {{9798331526276}},
issn = {{0743-1546}},
language = {{eng}},
pages = {{224--229}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{Proceedings of the IEEE Conference on Decision and Control}},
title = {{On the Stability of Dynamical Multi-Commodity Flow Networks}},
url = {{http://dx.doi.org/10.1109/CDC57313.2025.11312216}},
doi = {{10.1109/CDC57313.2025.11312216}},
year = {{2025}},
}