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

Tibor Szkaliczki (), Anita Sobe and Wilfried Elmenreich
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Tibor Szkaliczki: Hungarian Academy of Sciences
Anita Sobe: University of Neuchatel
Wilfried Elmenreich: Alpen-Adria-Universität Klagenfurt

Central European Journal of Operations Research, 2016, vol. 24, issue 4, No 9, 939-964

Abstract: 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.

Keywords: Self-organizing algorithm; Convergence; Markov chains (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10100-015-0412-9

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