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On Robustness of Equilibria in Transportation Networks

Stålberg, Rasmus (2018)
Department of Automatic Control
Abstract
As infrastructural systems become ever more complex and interconnected, they may also become ever more vulnerable to system-wide faults due to local disturbances. As such it is of great importance to design these system to be resilient, i.e. to be able to withstand and recover from disturbances or new conditions. In the case of traffic networks, while much work has been done to analyze the stability of these systems, there is still little work to analyze their resilience.
This thesis analyzes a variant of Daganzo’s Cell Transmisson Model to explore the robustness of equilibria in dynamical flow networks in response to various perturbations. In particular it tries to characterize the set of perturbations which force a freeflow equilibrium... (More)
As infrastructural systems become ever more complex and interconnected, they may also become ever more vulnerable to system-wide faults due to local disturbances. As such it is of great importance to design these system to be resilient, i.e. to be able to withstand and recover from disturbances or new conditions. In the case of traffic networks, while much work has been done to analyze the stability of these systems, there is still little work to analyze their resilience.
This thesis analyzes a variant of Daganzo’s Cell Transmisson Model to explore the robustness of equilibria in dynamical flow networks in response to various perturbations. In particular it tries to characterize the set of perturbations which force a freeflow equilibrium out of freeflow. Since any such equilibrium is locally asymptotically stable, the retention of freeflow would thus ensure a retention of stability.
The report first finds the smallest necessary size (in ℓ1-norm and for arbitrary affine cost functions) of any deterministic perturbations to the exogenous inflows to violate freeflow. Second it finds bounds for the probability of the equilibrium flows to violate freeflow due to stochastic exogenous inflows; either normally or independent, exponentially distributed. Third it finds the new equilibrium matrix and a
condition for the retention of freeflow following a single-cell routing perturbation. Finally it simulates a simple network’s performance in response to periodic exogenous inflows and cell mass increments, where it is shown that exogenous inflows with feasible averages may still cause system-wide faults and that mass increments are more disruptive the further away the affected cell is from a drain cell. (Less)
Please use this url to cite or link to this publication:
author
Stålberg, Rasmus
supervisor
organization
year
type
H3 - Professional qualifications (4 Years - )
subject
report number
TFRT-6066
ISSN
0280-5316
language
English
id
8958996
date added to LUP
2018-10-29 10:44:35
date last changed
2018-10-29 10:44:35
@misc{8958996,
  abstract     = {{As infrastructural systems become ever more complex and interconnected, they may also become ever more vulnerable to system-wide faults due to local disturbances. As such it is of great importance to design these system to be resilient, i.e. to be able to withstand and recover from disturbances or new conditions. In the case of traffic networks, while much work has been done to analyze the stability of these systems, there is still little work to analyze their resilience.
 This thesis analyzes a variant of Daganzo’s Cell Transmisson Model to explore the robustness of equilibria in dynamical flow networks in response to various perturbations. In particular it tries to characterize the set of perturbations which force a freeflow equilibrium out of freeflow. Since any such equilibrium is locally asymptotically stable, the retention of freeflow would thus ensure a retention of stability.
 The report first finds the smallest necessary size (in ℓ1-norm and for arbitrary affine cost functions) of any deterministic perturbations to the exogenous inflows to violate freeflow. Second it finds bounds for the probability of the equilibrium flows to violate freeflow due to stochastic exogenous inflows; either normally or independent, exponentially distributed. Third it finds the new equilibrium matrix and a
condition for the retention of freeflow following a single-cell routing perturbation. Finally it simulates a simple network’s performance in response to periodic exogenous inflows and cell mass increments, where it is shown that exogenous inflows with feasible averages may still cause system-wide faults and that mass increments are more disruptive the further away the affected cell is from a drain cell.}},
  author       = {{Stålberg, Rasmus}},
  issn         = {{0280-5316}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{On Robustness of Equilibria in Transportation Networks}},
  year         = {{2018}},
}