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

Author

Listed:
  • Tibor Szkaliczki

    (Hungarian Academy of Sciences)

  • Anita Sobe

    (University of Neuchatel)

  • Wilfried Elmenreich

    (Alpen-Adria-Universität Klagenfurt)

Abstract

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.

Suggested Citation

  • Tibor Szkaliczki & Anita Sobe & Wilfried Elmenreich, 2016. "Convergence and monotonicity of the hormone levels in a hormone-based content delivery system," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(4), pages 939-964, December.
    • Handle: RePEc:spr:cejnor:v:24:y:2016:i:4:d:10.1007_s10100-015-0412-9
    DOI: 10.1007/s10100-015-0412-9
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    References listed on IDEAS

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    1. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
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