Visible to the public Analysis on Convergence of Stochastic Processes in Cloud Computing Models

TitleAnalysis on Convergence of Stochastic Processes in Cloud Computing Models
Publication TypeConference Paper
Year of Publication2018
AuthorsNie, J., Tang, H., Wei, J.
Conference Name2018 14th International Conference on Computational Intelligence and Security (CIS)
Keywordsarbitrary stochastic processes, Biological system modeling, cloud computing, cloud computing models, cloud computing systems, common stochastic processes, complicated model, Computational modeling, convergence, Eigenvalues and eigenfunctions, Markov processes, matrix algebra, matrix-defined systems, pubcrawl, Rate of Convergence, Resiliency, resource allocation, resource allocations, Scalability, security, Steady-state, Stochastic computing, stochastic matrices, stochastic matrix, Stochastic Process, Stochastic processes
AbstractOn cloud computing systems consisting of task queuing and resource allocations, it is essential but hard to model and evaluate the global performance. In most of the models, researchers use a stochastic process or several stochastic processes to describe a real system. However, due to the absence of theoretical conclusions of any arbitrary stochastic processes, they approximate the complicated model into simple processes that have mathematical results, such as Markov processes. Our purpose is to give a universal method to deal with common stochastic processes as long as the processes can be expressed in the form of transition matrix. To achieve our purpose, we firstly prove several theorems about the convergence of stochastic matrices to figure out what kind of matrix-defined systems has steady states. Furthermore, we propose two strategies for measuring the rate of convergence which reflects how fast the system would come to its steady state. Finally, we give a method for reducing a stochastic matrix into smaller ones, and perform some experiments to illustrate our strategies in practice.
Citation Keynie_analysis_2018