Models of structural coherence in telecommunication systems - Popovsky, V. V. (ХНУРЭ, 2013)
Mathematical models of structural connectivity for fixed and dynamic systems are considered. Ezary-Proshan and Polessky estimations are given for fixed systems while for dynamic systems these estimations are determined in the state space. Quality of state estimation under different connectivity of vector components of dynamic system nodes is analyzed. It is shown that Tchebotarev-Achaev basic model approaches the procedure of stochastic synchronization of states. The presence of connectivity in the network structures, such as infocommunication systems, provides the acquisition of properties for the reliability and survivability of networks. For fixed (invariable with time parameters) networks connection is displayed as connectivity matrix, which may have a binary structure or consist of quantitative data de-fining the level of the connection (probability, number of channels, distance, etc.). The co-efficient of connectivity or connectivity probability for such networks is found by the approximate methods of Ezary-Proschan, Polesski etc. For dynamic (with time-varying elements of connection) network connectivity values can be obtained through the current assessment of the state of connectivity for each node from all adjacent nodes. For real posteriori evaluation of connectivity it is appropriate to use the state-space model that allows us to characterize the dynamic systems as deterministic and stochastic. Practice has shown that the state of the process allows to use the methods of stochastic approximation under the condition of choosing the sampling rate. The analysis of multi-dimensional differential systems shows that the existence of connections between components of the system cannot have arbitrary values. A large number of connections leads to unstable regimes. In the other extreme case: under the absence of reciprocal connection the system loses its system properties (integrity, emergence). The connection between random processes improves accuracy (reduced values of a posterior variance) of the estimates of the components for these processes compared to that case when data of the process are independent.
Keywords: connectivity; state; evaluation