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Department of Mathematics

Photo: UHH/Denstorf

Local stabilization of large unstable networks

The investigation in this project is motivated by the following observation: In large and complex networks, unstable subnetworks often occur due to local overload or due to non-availability of nodes or links, but nevertheless, there co-exist regions where other subnetworks stabilize locally. Due to the local instability the describing Markovian network processes are generically non-ergodic. Nevertheless it can be seen that locally, i.e., for some subset of nodes the local processes, which are not Markovian of their own, converge to a well defined stochastic limit.
Additionally, we investigate the impact of unreliability of nodes on the stabilization of networks or subnetworks.
Recent applications, where nodes or links may be not available for some time, are mobile and ad-hoc networks or sensor networks. The emergence of wireless ad-hoc networks, which are built of varying sets of mobile users with wireless communication capabilities without relying on a pre-existing infrastructure, introduces problems concerning availability of transmission nodes in the vicinity of a user. On the other hand, in such networks, overload emerges from too many users entering a region and applying for transmission.
Collaboration with Jennifer Mylosz (University of Hamburg) and Bernd Heidergott (Vrije Universiteit Amsterdam).

Some recent articles concerning Local stabilization of large unstable networks:

  1. Non-ergodic Jackson networks with infinite supply – local stabilization and local equilibrium analysis (with Jennifer Sommer and Bernd Heidergott)
    Journal of Applied Probability 53(4), 1125 – 1142, 2016
  2. On the behavior of stable subnetworks in non-ergodic networks with unreliable nodes (with Jennifer Mylosz)
    Computer Networks 53 (8), 1249–1263, 2009
  3. On the behavior of stable subnetworks in non-ergodic networks: A quasi-stationary approach in a two-node system (with Jennifer Mylosz)
    in: Wolfinger, B. E. and Heidtmann, K.-D. (eds.): Leistungs–, Zuverlässigkeits und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen, 6. GI/NTG–Workshop MMBnet 2011
    Berichte des Fachbereichs Informatik der Universität Hamburg No. 298, 99–106, Hamburg 2011.