Analyses with Index Matrices Mathematical Models of Network Systems

The large amount of information nowadays requires building Data Centers and implementation of optimization models for storing and transferring data. The requirement of limited time of processing the network requests, are needed proper ways of redirection of data and application of algorithms programmatically in different levels. Before this, a data has to be gathered under different circumstances and to be checked if the information has been transferred successfully or not and then based on the results the counts of successful and not successful outcomes to presented and compared with predicate theory. There are many probability models, with which can be analyzed and predicted future events. In this article with the Theory of Index matrices, Graph theory and Theory of probabilities will be analyzed a stochastic process for modeling the times at which flows of a network enter a system. Because the network traffic depends on time, different scenarios of communication durations such as intrinsic time interval and endogenous jump time, will be considered and evaluated if they perform a certain condition. The most proper results of the experiments, which will be calculated with linear and exponential functions and represented with different Index matrices, can be used in machine learning of Data Center Networks.