Mean-field Macro Computation in Large-scale Cloud Service Systems with Resource Management and Job Scheduling
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Service computing is an emerging and distributed computing mode in cloud service systems, and has become an interesting research direction for both academia and industry. Note that the cloud service systems always display new characteristics, such as stochasticity, large scale, loose coupling, concurrency, non-homogeneity and heterogeneity, thus their load balancing investigation has been more interesting, difficult and challenging until now. By using resource management and job scheduling, this paper proposes an integrated, real-time and dynamic control mechanism for large-scale cloud service systems and their load balancing through combining supermarket models with not only work stealing models but also scheduling of public reserved resource. To this end, this paper provides a novel stochastic model with weak interactions by means of nonlinear Markov processes. To overcome theoretical difficulties growing out of the state explosion in high-dimensional stochastic systems, this paper applies the mean-field theory to develop a macro computational technique in terms of an infinite-dimensional system of mean-field equations. Furthermore, this paper proves the asymptotic independence of the large-scale cloud service system, and show how to compute the fixed point by virtue of an infinite-dimensional system of nonlinear equations. Based on the fixed point, this paper provides effective numerical computation for performance analysis of this system under a high approximate precision. Therefore, we hope that the methodology and results given in this paper can be applicable to the study of more general large-scale cloud service systems.
KeywordsLarge-scale cloud service system resource management job scheduling supermarket model work stealing model scheduling of public reserved resource
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The authors are grateful to the editor and two anonymous referees for their constructive comments and suggestions, which sufficiently help the authors to improve the presentation of this manuscript. In addition, Yanping Jiangwas supported by the National Natural Science Foundation of China under grant Nos. 71871048 and 71571040; and Quanlin Li was supported by the National Natural Science Foundation of China under grant Nos. 71671158 and 71471160, and by the Natural Science Foundation of Hebei province under grant No. G2017203277.
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