Central European Journal of Operations Research

, Volume 24, Issue 4, pp 939–964 | Cite as

Convergence and monotonicity of the hormone levels in a hormone-based content delivery system

  • Tibor Szkaliczki
  • Anita Sobe
  • Wilfried Elmenreich
Original Paper


The practical significance of bio-inspired, self-organising methods is rapidly increasing due to their robustness, adaptability and capability of handling complex tasks in a dynamically changing environment. Our aim is to examine an artificial hormone system that was introduced in order to deliver multimedia content in dynamic networks. The artificial hormone algorithm proved to be an efficient approach to solve the problem during the experimental evaluations. In this paper we focus on the theoretical foundation of its goodness. We show that the hormone levels converge to a limit at each node in the typical cases. We form a series of theorems on convergence with different conditions which are built on each other by starting with a specific base case and then we consider more general, practically relevant cases. The theorems are proved by exploiting the analogy between the Markov chains and the artificial hormone system. We examine spatial and temporal monotonicity of the hormone levels as well and give sufficient conditions on monotonic increase.


Self-organizing algorithm Convergence Markov chains 



Research is supported by the Hungarian National Development Agency under Grant HUMAN_MB08-1-2011-0010. Special thanks are due to Katalin Friedl and László Böszörmenyi for the consultations on the hormone algorithms and the convergence.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Tibor Szkaliczki
    • 1
  • Anita Sobe
    • 2
  • Wilfried Elmenreich
    • 3
  1. 1.Institute for Computer Science and ControlHungarian Academy of SciencesBudapestHungary
  2. 2.Department of Computer ScienceUniversity of NeuchatelNeuchâtelSwitzerland
  3. 3.Institute of Networked and Embedded Systems/Lakeside LabsAlpen-Adria-Universität KlagenfurtKlagenfurt am WörtherseeAustria

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