The Cyber-Physical-Social Transition Tensor Service Framework

Cyber-Physical-Social Systems (CPSS) are the extension of Cyber-Physical Systems (CPS) which integrate social characteristics into Cyber-Physical Systems. The emergence of CPSS provides a promising solution for energy and sustainability challenges, at the same time, CPSS make sustainability computing space change from single space to multi-spaces. To cope with the problem, we propose Cyber-Physical-Social Transition Tensor service framework to provide sustainable services for multi-spaces. To the best of our knowledge, this is the first framework that can support multi-space services at one time. The framework solves various stationary probability distributions arising from the multi-relational data from CPSS, then provides services for multi-spaces based on the probability distributions. In order to solve the stationary probability distributions, we develop a novel iterative algorithm, named Intersect Tensor Power Method (ITPM). Furthermore, we prove the convergence of the iterative algorithm, the existence and uniqueness of the stationary probability distribution. This paper's highlight is the Cyber-Physical-Social Transition Tensor (CPST
²
) model which leverages multivariate transition tensor to seamlessly integrate massive data from CPSS. A case study of multi-space prediction service illustrates our framework, the accuracy reaches 95 percent with three kinds of humans, two hundred and fifty traffic flow slices, and nineteen time slices.