Abstract
With the advent of the Internet of Things (IoT) as a major force of change in industry, Cyber Physical Systems (CPS) is right for building the concept smart Environment. In CPS, the internal computational and physical elements generally interact, reflect and influence each other in order to obtain and analyze human behaviors and their social activities, finally to help them facilitate experiences. Nevertheless, the system complexity and scale become challenges of discrete state modelling formalisms especially in the capability issue. For the stochastic process algebra, performance evaluation process algebra (PEPA), a fluid approximation approach dealing with this problem has been developed, which approximates the continuous time Markov chain underlying a model using ordinary differential equations (ODEs). This paper establishes some basic properties for the ODE based approximation, e.g., uniqueness, existence and boundedness of ODE solutions. Our research in particular presents a convergence of the solutions for nonsynchronised models.
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Notes
- 1.
This CTMC is essentially the same to the “standard” CTMC.
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Acknowledgements
The authors acknowledge the financial support by the NSF of China under Grant No 61472343, and the NSF of Jiangsu Province of China under Grant BK20151314 and BK20160543.
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Ding, J., Chen, X., Zhu, X. (2018). Analysis of the Fluid Approximation of Stochastic Process Algebra Models. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2017 Chinese Intelligent Systems Conference. CISC 2017. Lecture Notes in Electrical Engineering, vol 459. Springer, Singapore. https://doi.org/10.1007/978-981-10-6496-8_16
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DOI: https://doi.org/10.1007/978-981-10-6496-8_16
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