Stability and phase transitions of dynamical flow networks with finite capacities
(2020) In IFAC-PapersOnLine 53(2). p.2588-2593- Abstract
- We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell —consisting of the difference between the total flow directed towards it minus the outflow from it— exceeds a certain capacity constraint, then the exceeding part of it leaks out of the system. The ensuing network flow dynamics is a linear saturated system with compact state space that we analyse using tools from monotone systems and contraction theory. Specifically, we prove that there exists a set of equilibrium points that is globally asymptotically stable. Such set of equilibrium points reduces to a single globally... (More)
- We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell —consisting of the difference between the total flow directed towards it minus the outflow from it— exceeds a certain capacity constraint, then the exceeding part of it leaks out of the system. The ensuing network flow dynamics is a linear saturated system with compact state space that we analyse using tools from monotone systems and contraction theory. Specifically, we prove that there exists a set of equilibrium points that is globally asymptotically stable. Such set of equilibrium points reduces to a single globally asymptotically stable equilibrium point for generic exogenous demand vectors. Moreover, we show that the critical exogenous demand vectors giving rise to non-unique equilibrium points correspond to phase transitions in the asymptotic behavior of the dynamical flow network. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/018a2896-8326-41f0-bcbf-b63269e7e662
- author
- Massai, Leonardo ; Como, Giacomo LU and Fagnani, Fabio
- organization
- publishing date
- 2020-01-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- IFAC-PapersOnLine
- volume
- 53
- issue
- 2
- pages
- 2588 - 2593
- publisher
- IFAC Secretariat
- external identifiers
-
- scopus:85105078784
- ISSN
- 2405-8963
- DOI
- 10.1016/j.ifacol.2020.12.306
- project
- Dynamics of Complex Socio-Technological Network Systems
- language
- English
- LU publication?
- yes
- id
- 018a2896-8326-41f0-bcbf-b63269e7e662
- alternative location
- https://linkinghub.elsevier.com/retrieve/pii/S2405896320305875
- date added to LUP
- 2022-02-14 17:33:10
- date last changed
- 2022-04-25 08:55:54
@article{018a2896-8326-41f0-bcbf-b63269e7e662,
abstract = {{We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell —consisting of the difference between the total flow directed towards it minus the outflow from it— exceeds a certain capacity constraint, then the exceeding part of it leaks out of the system. The ensuing network flow dynamics is a linear saturated system with compact state space that we analyse using tools from monotone systems and contraction theory. Specifically, we prove that there exists a set of equilibrium points that is globally asymptotically stable. Such set of equilibrium points reduces to a single globally asymptotically stable equilibrium point for generic exogenous demand vectors. Moreover, we show that the critical exogenous demand vectors giving rise to non-unique equilibrium points correspond to phase transitions in the asymptotic behavior of the dynamical flow network.}},
author = {{Massai, Leonardo and Como, Giacomo and Fagnani, Fabio}},
issn = {{2405-8963}},
language = {{eng}},
month = {{01}},
number = {{2}},
pages = {{2588--2593}},
publisher = {{IFAC Secretariat}},
series = {{IFAC-PapersOnLine}},
title = {{Stability and phase transitions of dynamical flow networks with finite capacities}},
url = {{http://dx.doi.org/10.1016/j.ifacol.2020.12.306}},
doi = {{10.1016/j.ifacol.2020.12.306}},
volume = {{53}},
year = {{2020}},
}