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A multi-commodity dynamical model for traffic networks

Nilsson, Gustav (2013) In ISSN 0280-5316
Department of Automatic Control
Abstract
A dynamical model for traffic networks is proposed and analyzed. In the traffic network, the transportation demands are considered as multi-commodity flows where each commodity has a unique destination. The network is modeled by a multigraph where at each node each commodity splits among the outgoing links in a way such that the drivers are more likely to avoid a road when the density on it increases. It will be shown that if the graph has no cycles, the density of each commodity on each link will converge to a unique limit that does not depend on the initial state.
Network resilience, namely structural robustness of the network with respect to perturbations, is also studied. In particular, it is shown that if all commodities have access... (More)
A dynamical model for traffic networks is proposed and analyzed. In the traffic network, the transportation demands are considered as multi-commodity flows where each commodity has a unique destination. The network is modeled by a multigraph where at each node each commodity splits among the outgoing links in a way such that the drivers are more likely to avoid a road when the density on it increases. It will be shown that if the graph has no cycles, the density of each commodity on each link will converge to a unique limit that does not depend on the initial state.
Network resilience, namely structural robustness of the network with respect to perturbations, is also studied. In particular, it is shown that if all commodities have access to all outgoing links, the network can manage perturbations whose magnitude is less than a quantity which plays the natural role of residual capacity of an equilibrium. If instead not all commodities have access to all links, overreaction of the network to perturbations implies that even small perturbations might be amplified
and start a cascade.
Finally, the idea of back-pressure is employed to provide a simple distributed control strategy. Analogously to the single commodity case, such actual strategy is able to back-propagate the information that congestion is happening ahead, thus allowing the drivers to reroute even if their decision is based on local information only. (Less)
Please use this url to cite or link to this publication:
author
Nilsson, Gustav
supervisor
organization
year
type
H3 - Professional qualifications (4 Years - )
subject
publication/series
ISSN 0280-5316
other publication id
ISRN LUTFD2/TFRT--5925--SE
language
English
additional info
month=august
id
4000930
date added to LUP
2013-08-26 12:05:11
date last changed
2013-08-26 12:05:11
@misc{4000930,
  abstract     = {A dynamical model for traffic networks is proposed and analyzed. In the traffic network, the transportation demands are considered as multi-commodity flows where each commodity has a unique destination. The network is modeled by a multigraph where at each node each commodity splits among the outgoing links in a way such that the drivers are more likely to avoid a road when the density on it increases. It will be shown that if the graph has no cycles, the density of each commodity on each link will converge to a unique limit that does not depend on the initial state.
 Network resilience, namely structural robustness of the network with respect to perturbations, is also studied. In particular, it is shown that if all commodities have access to all outgoing links, the network can manage perturbations whose magnitude is less than a quantity which plays the natural role of residual capacity of an equilibrium. If instead not all commodities have access to all links, overreaction of the network to perturbations implies that even small perturbations might be amplified
and start a cascade.
 Finally, the idea of back-pressure is employed to provide a simple distributed control strategy. Analogously to the single commodity case, such actual strategy is able to back-propagate the information that congestion is happening ahead, thus allowing the drivers to reroute even if their decision is based on local information only.},
  author       = {Nilsson, Gustav},
  language     = {eng},
  note         = {Student Paper},
  series       = {ISSN 0280-5316},
  title        = {A multi-commodity dynamical model for traffic networks},
  year         = {2013},
}