Quantitative Modeling of Self-organizing Properties

For analyzing properties of complex systems, a mathematical model for these systems is useful. In this paper we give quantitative definitions of adaptivity, target orientation, homogeneity and resilience with respect to faulty nodes or attacks by intruders. The modeling of the system is done by using a multigraph to describe the connections between objects and stochastic automatons for the behavior of the objects. The quantitative definitions of the properties can help for the analysis of existing systems and for the design of new systems. To show the practical usability of the concepts, the definitions are applied to a slot synchronization algorithm in wireless sensor networks.

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