Robust distributed routing in dynamical networks -- Part I: Locally responsive policies and weak resilience
(2013) In IEEE Transactions on Automatic Control 58(2). p.317-332- Abstract
- Abstract in Undetermined
Robustness of distributed routing policies is studied for dynamical networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical network is modeled as a system of ordinary differential equations derived from mass conservation laws on a directed acyclic graph with a single origin-destination pair and a constant total outflow at the origin. Routing policies regulate the way the total outflow at each nondestination node gets split among its outgoing links as a function of the current particle density, while the outflow of a link is modeled to depend on the current particle density on that link through a flow function. The dynamical network is called partially transferring if... (More) - Abstract in Undetermined
Robustness of distributed routing policies is studied for dynamical networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical network is modeled as a system of ordinary differential equations derived from mass conservation laws on a directed acyclic graph with a single origin-destination pair and a constant total outflow at the origin. Routing policies regulate the way the total outflow at each nondestination node gets split among its outgoing links as a function of the current particle density, while the outflow of a link is modeled to depend on the current particle density on that link through a flow function. The dynamical network is called partially transferring if the total inflow at the destination node is asymptotically bounded away from zero, and its weak resilience is measured as the minimum sum of the link-wise magnitude of disturbances that make it not partially transferring. The weak resilience of a dynamical network with arbitrary routing policy is shown to be upper bounded by the network's min-cut capacity and, hence, is independent of the initial flow conditions. Moreover, a class of distributed routing policies that rely exclusively on local information on the particle densities, and are locally responsive to that, is shown to yield such maximal weak resilience. These results imply that locality constraints on the information available to the routing policies do not cause loss of weak resilience. Fundamental properties of dynamical networks driven by locally responsive distributed routing policies are analyzed in detail, including global convergence to a unique limit flow. The derivation of these properties exploits the cooperative nature of these dynamical systems, together with an additional stability property implied by the assumption of monotonicity of the flow as a function of the density on each link. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2294010
- author
- Como, Giacomo LU ; Savla, Ketan ; Acemoglu, Daron ; Dahleh, Munther A. and Frazzoli, Emilio
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- distributed routing policies, Cooperative dynamical systems, dynamical, networks, min-cut capacity, monotone control systems, weak resilience
- in
- IEEE Transactions on Automatic Control
- volume
- 58
- issue
- 2
- pages
- 317 - 332
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- wos:000314163100004
- scopus:84873848192
- ISSN
- 0018-9286
- DOI
- 10.1109/TAC.2012.2209951
- language
- English
- LU publication?
- yes
- additional info
- key=como_etal2011ieeeacI
- id
- a648abda-0728-47cd-8e91-c2045cede8e7 (old id 2294010)
- date added to LUP
- 2016-04-01 14:04:02
- date last changed
- 2024-04-10 14:47:39
@article{a648abda-0728-47cd-8e91-c2045cede8e7,
abstract = {{Abstract in Undetermined<br/>Robustness of distributed routing policies is studied for dynamical networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical network is modeled as a system of ordinary differential equations derived from mass conservation laws on a directed acyclic graph with a single origin-destination pair and a constant total outflow at the origin. Routing policies regulate the way the total outflow at each nondestination node gets split among its outgoing links as a function of the current particle density, while the outflow of a link is modeled to depend on the current particle density on that link through a flow function. The dynamical network is called partially transferring if the total inflow at the destination node is asymptotically bounded away from zero, and its weak resilience is measured as the minimum sum of the link-wise magnitude of disturbances that make it not partially transferring. The weak resilience of a dynamical network with arbitrary routing policy is shown to be upper bounded by the network's min-cut capacity and, hence, is independent of the initial flow conditions. Moreover, a class of distributed routing policies that rely exclusively on local information on the particle densities, and are locally responsive to that, is shown to yield such maximal weak resilience. These results imply that locality constraints on the information available to the routing policies do not cause loss of weak resilience. Fundamental properties of dynamical networks driven by locally responsive distributed routing policies are analyzed in detail, including global convergence to a unique limit flow. The derivation of these properties exploits the cooperative nature of these dynamical systems, together with an additional stability property implied by the assumption of monotonicity of the flow as a function of the density on each link.}},
author = {{Como, Giacomo and Savla, Ketan and Acemoglu, Daron and Dahleh, Munther A. and Frazzoli, Emilio}},
issn = {{0018-9286}},
keywords = {{distributed routing policies; Cooperative dynamical systems; dynamical; networks; min-cut capacity; monotone control systems; weak resilience}},
language = {{eng}},
number = {{2}},
pages = {{317--332}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Automatic Control}},
title = {{Robust distributed routing in dynamical networks -- Part I: Locally responsive policies and weak resilience}},
url = {{http://dx.doi.org/10.1109/TAC.2012.2209951}},
doi = {{10.1109/TAC.2012.2209951}},
volume = {{58}},
year = {{2013}},
}