Modeling long range dependent and fractal job traffic in data-intensive grids

In this paper we propose the application of the Mul-tifractal Wavelet Model (MWM) in modeling long range dependent and fractal job arrivals in data-intensive clus-ters and Grids. Job arrivals can be described as point processes and it is shown that correlations and the fractal behavior can only be reliably revealed using the count/rate process. Using real workload data from production Grids, we show that the second order properties such as the autocorrelation function (ACF) and the scaling of the count/rate processes can be well reconstructed by MWM modeling. A so-called controlled-variability integrate-and-fire (CV-InF) algorithm is adopted to transform a rate process into an interarrival process so that a full description of the arrival process can be obtained. Quan-tified by the transportation distance, the marginal dis-tributions of the rate and interarrival process can be matched approximately by the combined MWM and CV-InF model. It is further shown that the additive nature of rates makes it possible to model different patterns sep-arately and aggregate them back to form a whole unified process. This makes our approach general and flexible enough to incorporate various patterns and form a co-herent solution for Grid job arrivals at different levels.