Multifractal analysis of memory usage patterns

Abstract

The discovery of fractal phenomenon in computer-related areas such as network traffic flow leads to the hypothesis that many computer resources display fractal characteristics. The goal of this study is to apply fractal analysis to computer memory usage patterns. We devise methods for calculating the Hölder exponent of a time series and calculating the fractal dimension of a plot of a time series. These methods are then applied to memory-related data collected from a Unix server. We find that our methods for calculating the Hölder exponent of a time series yield results that are independently confirmed through calculation of the fractal dimension of the time series, and that computer memory use does indeed display multifractal behavior. In addition, it is hypothesized that this multifractal behavior may be useful in making certain predictions about the future behavior of an operating system.

Modeling operating system crash behavior through multifractal analysis, long range dependence and mining of memory usage patterns

“…Falconer in [9] and Crowell in [6] present the five properties of fractals as fine structure, irregularity, self-similarity, fractional dimension and recursive definition.…”

“…Crowell in [6] gives an algorithm to calculate the Hölder exponent for a time-series of discrete data points. This algorithm was developed by Dr. Mark Shereshevsky at West Virginia…”

“…This was setup using the Performance Logs and Alerts Utility. The log was setup to collect data on three parameters identified by Crowell[19][6], as being of interest by showing fractal behavior and not being strongly correlated to each other. This data was stored in a log file which was transferred to Server A and logged for further analysis.The experiment was run multiple times as described below in the Experiments and DataCollection section, with the time of crash ranging from a couple of hours to 5 days.…”

“…Data from other crash tests were then filtered through this decision tree to obtain predictions made by the M5' Model Tree based nominal classifier.The predicted value was the number of intervals to crash. These predicted values were then compared with actual time to crash and plotted on screen as a graph.4.5.4 Fractal Analysis 1.0This is a Java Swing based application that uses the initial classes developed by Crowell[6] with some modifications. The application plots the data values, generates and plots the multidimensional Hölder Exponent and it can compute and plot the Shewhart Series and Crash Prediction plots.…”

“…Multi-fractal analysis was applied to this three-dimensional data and certain points of fractal breakdown were identified and the second fractal breakdown was chosen to signal a dangerous level of resource exhaustion. That work however did not consider any investigation into analyzing the data using already existing machine learning algorithms for prediction of continuous classes[40][8].Most of the work done in[6] by Crowell involves parameter measurements on a UNIX system. A strong correlation between the fractality of a memory resource (lg alloc) and the workload event of system backup.…”