Extreme Value Analysis for Time-variable Mixed Workload

Proper timeliness is vital for a lot of real-world computing systems. Understanding the phenomena of extreme workloads is essential because unhandled, extreme workloads could cause violation of timeliness requirements, service degradation, and even downtime. Extremity can have multiple roots: (1) service requests can naturally produce extreme workloads; (2) bursts could randomly occur on a probabilistic basis in case of a mixed workload in multiservice systems; (3) workload spikes typically happen in deadline bound tasks.Extreme Value Analysis (EVA) is a statistical method for modeling the extremely deviant values corresponding to the largest values. The foundation mathematics of EVA, the Extreme Value Theorem, requires the dataset to be independent and identically distributed. However, this is not generally true in practice because, usually, real-life processes are a mixture of sources with identifiable patterns. For example, seasonality and periodic fluctuations are regularly occurring patterns. Deadlines can be purely periodic, e.g., monthly tax submissions, or time variable, e.g., university homework submission with variable semester time schedules.We propose to preprocess the data using time series decomposition to separate the stochastic process causing extreme values. Moreover, we focus on the case where the root cause of the extreme values is the same mechanism: a deadline. We exploit known deadlines using dynamic time warp to search for the recurring similar workload peak patterns varying in time and amplitude.

Softarisons: theory and practice

This paper introduces the concept of softarison. Softarisons merge soft set theory with the theory of binary relations. Their purpose is the comparison of alternatives in a parameterized environment. We develop the basic theory and interpretations of softarisons. Then, the normative idea of ‘optimal’ alternatives is discussed in this context. We argue that the meaning of ‘optimality’ can be adjusted to fit in with the structure of each problem. A sufficient condition for the existence of an optimal alternative for unrestricted sets of alternatives is proven. This result means a counterpart of Weierstrass extreme value theorem for softarisons; thus, it links soft topology with the act of choice. We also provide a decision-making procedure—the minimax algorithm—when the alternatives are compared through a softarison. A case-study in the context of group interviews illustrates both the application of softarisons as an evaluation tool, and the computation of minimax solutions.

Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization

Several new asymmetric distributions have arisen naturally in the modeling extreme values are uncovered and elucidated. The present paper deals with the extreme value theorem (EVT) under exponential normalization. An estimate of the shape parameter of the asymmetric generalized value distributions that related to this new extension of the EVT is obtained. Moreover, we develop the mathematical modeling of the extreme values by using this new extension of the EVT. We analyze the extreme values by modeling the occurrence of the exceedances over high thresholds. The natural distributions of such exceedances, new four generalized Pareto families of asymmetric distributions under exponential normalization (GPDEs), are described and their properties revealed. There is an evident symmetry between the new obtained GPDEs and those generalized Pareto distributions arisen from EVT under linear and power normalization. Estimates for the extreme value index of the four GPDEs are obtained. In addition, simulation studies are conducted in order to illustrate and validate the theoretical results. Finally, a comparison study between the different extreme models is done throughout real data sets.