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Non-equilibrium Solutions of Dynamic Networks: A Hybrid System Approach

  • Scott GreenhalghEmail author
  • Monica-Gabriela Cojocaru
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 113)

Abstract

Many dynamic networks can be analyzed through the framework of equilibrium problems. While traditionally, the study of equilibrium problems is solely concerned with obtaining or approximating equilibrium solutions, the study of equilibrium problems not in equilibrium provides valuable information into dynamic network behavior. One approach to study such non-equilibrium solutions stems from a connection between equilibrium problems and a class of parametrized projected differential equations. However, there is a drawback of this approach: the requirement of observing distributions of demands and costs. To address this problem we develop a hybrid system framework to model non-equilibrium solutions of dynamic networks, which only requires point observations. We demonstrate stability properties of the hybrid system framework and illustrate the novelty of our approach with a dynamic traffic network example.

Keywords

Dynamic networks Hybrid systems Variational inequalities Equilibrium problems 

Notes

Acknowledgements

Scott Greenhalgh and Monica-Gabriela Cojocaru would like to thank the referees comments which led to a clearer presentation of this work. Monica-Gabriela Cojocaru graciously acknowledges the support received from the Natural Sciences and Engineering Research Council (NSERC) of Canada.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Queen’s UniversityKingstonCanada
  2. 2.Univerity of GuelphGuelphCanada

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