Self-Learning Cloud Controllers: Fuzzy Q-Learning for Knowledge Evolution

Cloud controllers aim at responding to application demands by automatically scaling the compute resources at runtime to meet performance guarantees and minimize resource costs. Existing cloud controllers often resort to scaling strategies that are codified as a set of adaptation rules. However, for a cloud provider, applications running on top of the cloud infrastructure are more or less black-boxes, making it difficult at design time to define optimal or pre-emptive adaptation rules. Thus, the burden of taking adaptation decisions often is delegated to the cloud application. Yet, in most cases, application developers in turn have limited knowledge of the cloud infrastructure. In this paper, we propose learning adaptation rules during runtime. To this end, we introduce FQL4KE, a self-learning fuzzy cloud controller. In particular, FQL4KE learns and modifies fuzzy rules at runtime. The benefit is that for designing cloud controllers, we do not have to rely solely on precise design-time knowledge, which may be difficult to acquire. FQL4KE empowers users to specify cloud controllers by simply adjusting weights representing priorities in system goals instead of specifying complex adaptation rules. The applicability of FQL4KE has been experimentally assessed as part of the cloud application framework ElasticBench. The experimental results indicate that FQL4KE outperforms our previously developed fuzzy controller without learning mechanisms and the native Azure auto-scaling

Convergence of Fuzzy Tori and Quantum Tori for the quantum Gromov-Hausdorff Propinquity: an explicit approach

Quantum tori are limits of finite dimensional C*-algebras for the quantum Gromov-Hausdorff propinquity, a metric defined by the author as a strengthening of Rieffel's quantum Gromov-Hausdorff designed to retain the C*-algebraic structure. In this paper, we propose a proof of the continuity of the family of quantum and fuzzy tori which relies on explicit representations of the C*-algebras rather than on more abstract arguments, in a manner which takes full advantage of the notion of bridge defining the quantum propinquity.Comment: 41 Pages. This paper is the second half of ArXiv:1302.4058v2. The latter paper has been divided in two halves for publications purposes, with the first half now the current version of 1302.4058, which has been accepted in Trans. Amer. Math. Soc. This second half is now a stand-alone paper, with a brief summary of 1302.4058 and a new introductio