KPC-Toolbox: Best recipes for automatic trace fitting using Markovian Arrival Processes

Abstract

We present the KPC-Toolbox, a library of MATLAB scripts for fitting workload traces into Markovian Arrival Processes (MAPs) in an automatic way based on the recently proposed Kronecker Product Composition (KPC) method. We first present detailed sensitivity analysis that builds intuition on which trace descriptors are the most important for queueing performance, stressing the advantages of matching higher-order correlations of the process rather than higher-order moments of the distribution. Given that the MAP parameterization space can be very large, we focus on first determining the order of the smallest MAP that can fit the trace well using the Bayesian Information Criterion (BIC). The KPC-Toolbox then automatically derives a MAP that captures accurately the most essential features of the trace. Extensive experimentation illustrates the effectiveness of the KPC-Toolbox in fitting traces that are well documented in the literature as very challenging to fit, showing that the KPC-Toolbox offers a simple and powerful solution to fitting accurately trace data into MAPs. We provide a characterization of moments and correlations that can be fitted exactly by KPC, thus showing the wider applicability of the method compared to small order MAPs. We also consider the fitting of phase-type (PH-type) distributions, which are an important specialization of MAPs that are useful for describing traces without correlations in their time series. We illustrate that the KPC methodology can be easily adapted to PH-type fitting and present experimental results on networking and disk drive traces showing that the KPC-Toolbox can also match accurately higher-order moments of the inter-arrival times in place of correlations.