Quantitative Modeling of Self-organizing Properties

Abstract

Abstract. 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.

Emergence of Global Speed Patterns in a Traffic Scenario

“…The goal of a system [4] can be specified by a fitness function f : Conf → [0, 1] on the global state space. The fitness function describes, which configurations are good (f (c) ≈ 1) and which configurations are bad (f (c) ≈ 0).…”

“…In the recent years, some quantitative measures for properties in self-organizing systems have been developed [3], [4], [5]:…”

“…Analogously the emergence measure can also be applied to flow data (temporal density) to detect dependencies in flow data. The measure for target orientation [4] shows, whether the overall goal (traffic safety) is satisfied. The goal is formally specified by using the variance coefficient of velocities (see [7] and [2]).…”

The Degree of Global-State Awareness in Self-Organizing Systems

“…Several formal measures have been proposed for describing certain properties of SOSs, like autonomy [3,4], emergence [3,4,5], adaptivity, homogeneity, and resilience [6]. However, these measures do not evaluate to which extent the entities can derive the necessary global-state information from the information provided by their vicinity.…”

“…These system candidates can then be further investigated, e.g., by the method proposed in [2], towards how the entities can use the provided information in a purposeful, target-oriented manner. The resulting system can finally be evaluated by using the measure of target orientation proposed in [6].…”