An improved Brown's method applying fractal dimension to forecast the load in a computing cluster for short time series

Abstract

Background/Objectives: The study considers the class of short time series possessing persistency. The investigation is focused on selecting and adapting mathematical tools to forecast such type of time series. Methods/Statistical Analysis: Adaptive prediction models are capable of adjusting their structures and parameters to changing conditions. Adaptive prediction methods opted for Brown's method for time series of the load in a computing cluster. The time series under investigation possess persistency. Fractal dimension of time series should be defined applying the Hurst exponent averaged through these time series. The obtained fractal dimension should be taken as the smoothing ratio for Brown's method. Findings: Applied forecasting tasks are often comprised of too short samples that do not allow obtaining statistically valid predictions. To forecast short time series is a problem of current importance; and to solve this problem it is required to have an idea of the process described by these time series. One of such series is dynamic measurement of load in a computing cluster, the statistics of which cannot be modeled for a long-term period. In Brown's method, the predicted value is found applying the average weighted smoothing ratio within the range from zero to one. Selection of optimum smoothing ratio is mostly done experimentally, by sorting out all possible values within this range. This procedure can become quite labor-intensive. Besides, there were ideas of more precise forecasting if the smoothing ratio is selected within the range from one to two. This suggestion has to be justified. This study offers a prediction method improving Brown's method and confirms that the smoothing ratio should be selected within the range from one to two. Improvements/Applications: The suggested method provides theoretically precise calculated value of the smoothing ratio instead of the experimentally selected one and solves the problem of the measuring lag between forecast and actual values