Distributed Tracing for Troubleshooting of Native Cloud Applications via Rule-Induction Systems

Diagnosing IT issues is a challenging problem for large-scale distributed cloud environments due to complex and non-deterministic interrelations between the system components. Modern monitoring tools rely on AI-empowered data analytics for detection, root cause analysis, and rapid resolution of performance degradation. However, the successful adoption of AI solutions is anchored on trust. System administrators will not unthinkingly follow the recommendations without sufficient interpretability of solutions. Explainable AI is gaining popularity by enabling improved confidence and trust in intelligent solutions. For many industrial applications, explainable models with moderate accuracy are preferable to highly precise black-box ones. This paper shows the benefits of rule-induction classification methods, particularly RIPPER, for the root cause analysis of performance degradations. RIPPER reveals the causes of problems in a set of rules system administrators can use in remediation processes. Native cloud applications are based on the microservices architecture to consume the benefits of distributed computing. Monitoring such applications can be accomplished via distributed tracing, which inspects the passage of requests through different microservices. We discuss the application of rule-learning approaches to trace traffic passing through a malfunctioning microservice for the explanations of the problem. Experiments performed on datasets from cloud environments proved the applicability of such approaches and unveiled the benefits

Challenges and Experiences in Designing Interpretable KPI-diagnostics for Cloud Applications

Automated root cause analysis of performance problems in modern cloud computing infrastructures is of a high technology value in the self-driving context. Those systems are evolved into large scale and complex solutions which are core for running most of today’s business applications. Hence, cloud management providers realize their mission through a “total” monitoring of data center flows thus enabling a full visibility into the cloud. Appropriate machine learning methods and software products rely on such observation data for real-time identification and remediation of potential sources of performance degradations in cloud operations to minimize their impacts. We describe the existing technology challenges and our experiences while working on designing problem root cause analysis mechanisms which are automatic, application agnostic, and, at the same time, interpretable for human operators to gain their trust. The paper focuses on diagnosis of cloud ecosystems through their Key Performance Indicators (KPI). Those indicators are utilized to build automatically labeled data sets and train explainable AI models for identifying conditions and processes “responsible” for misbehaviors. Our experiments on a large time series data set from a cloud application demonstrate that those approaches are effective in obtaining models that explain unacceptable KPI behaviors and localize sources of issues

On a pointwise convergence of trigonometric interpolations with shifted nodes

We consider trigonometric interpolations with shifted equidistant nodes and investigate their accuracies depending on the shift parameter. Two different types of interpolations are in the focus of our attention: the Krylov-Lanczos and the rational-trigonometric-polynomial interpolations. The Krylov-Lanczos interpolation performs convergence acceleration of the classical trigonometric interpolation by polynomial corrections. Additional acceleration is achieved by application of rational corrections which contain some extra parameters. In both cases, we derive the exact constants of the asymptotic errors and, based on these estimates, we find the optimal shifts that provide with the best accuracy. Optimizations are performed for the pointwise convergence in the regions away from the endpoints. Asymptotic estimates allow optimal selection of the extra parameters in the rational corrections which provides with additional accuracy. Results of numerical experiments clarify theoretical investigations

On some optimizations of trigonometric interpolation using Fourier discrete coefficients

We investigate convergence of the rational-trigonometric-polynomial interpolations which perform convergence acceleration of the classical trigonometric interpolation by sequential application of polynomial and rational corrections. Rational corrections contain unknown parameters which determination outlines the behavior of the interpolations in different frameworks. We consider approach for determination of the unknown parameters by minimization of the constants of the asymptotic errors. We perform theoretical and numerical analysis of such optimal interpolations

On a convergence of the Fourier-Pade approximation

We consider convergence acceleration of the truncated Fourier series by sequential application of polynomial and rational corrections. Polynomial corrections are performed along the ideas of the Krylov-Lanczos approximation. Rational corrections contain unknown parameters which determination is a crucial problem for realization of the rational approximations. We consider approach connected with the Fourier-Pade approximations. This rational-trigonometric-polynomial approximation we continue calling the Fourier-Pade approximation. We investigate its convergence for smooth functions in different frameworks and derive the exact constants of asymptotic errors. Detailed analysis and comparisons of different rational-trigonometric-polynomial approximations are performed and the convergence properties of the Fourier-Pade approximation are outlined. In particular, fast convergence of the Fourier-Pade approximation is observed in the regions away from the endpoints

On a convergence of the Fourier-Pade approximation

We consider convergence acceleration of the truncated Fourier series by sequential application of polynomial and rational corrections. Polynomial corrections are performed along the ideas of the Krylov-Lanczos approximation. Rational corrections contain unknown parameters which determination is a crucial problem for realization of the rational approximations. We consider approach connected with the Fourier-Pade approximations. This rational-trigonometric-polynomial approximation we continue calling the Fourier-Pade approximation. We investigate its convergence for smooth functions in different frameworks and derive the exact constants of asymptotic errors. Detailed analysis and comparisons of different rational-trigonometric-polynomial approximations are performed and the convergence properties of the Fourier-Pade approximation are outlined. In particular, fast convergence of the Fourier-Pade approximation is observed in the regions away from the endpoints

Asymptotic estimates for the quasi-periodic interpolations

We investigate the convergence of the quasi-periodic interpolation on the entire interval $[-1,1]$ in the $L_2$-norm and at the endpoints of the interval by the limit function behavior. In both cases we derive exact constants for the main terms of the asymptotic errors. The results of numerical experiments confirm theoretical estimates and show the behavior of the quasi-periodic interpolation for specific functions

On a convergence of the Fourier-Pade approximation

We consider convergence acceleration of the truncated Fourier series by sequential application of polynomial and rational corrections. Polynomial corrections are performed along the ideas of the Krylov-Lanczos approximation. Rational corrections contain unknown parameters which determination is a crucial problem for realization of the rational approximations. We consider approach connected with the Fourier-Pade approximations. This rational-trigonometric-polynomial approximation we continue calling the Fourier-Pade approximation. We investigate its convergence for smooth functions in different frameworks and derive the exact constants of asymptotic errors. Detailed analysis and comparisons of different rational-trigonometric-polynomial approximations are performed and the convergence properties of the Fourier-Pade approximation are outlined. In particular, fast convergence of the Fourier-Pade approximation is observed in the regions away from the endpoints