On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
On approximating higher order MAPs with MAPs of order two
Queueing Systems: Theory and Applications
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
An EM-based technique for approximating long-tailed data sets with PH distributions
Performance Evaluation - Internet performance symposium (IPS 2002)
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Correlation bounds for second-order MAPs with application to queueing network decomposition
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Long-Range Dependence at the Disk Drive Level
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Efficient phase-type fitting with aggregated traffic traces
Performance Evaluation
Performance impacts of autocorrelated flows in multi-tiered systems
Performance Evaluation
A minimal representation of Markov arrival processes and a moments matching method
Performance Evaluation
Queueing Theory: A Linear Algebraic Approach
Queueing Theory: A Linear Algebraic Approach
On the canonical representation of phase type distributions
Performance Evaluation
Trace data characterization and fitting for Markov modeling
Performance Evaluation
Explicit inverse characterizations of acyclic MAPs of second order
EPEW'06 Proceedings of the Third European conference on Formal Methods and Stochastic Models for Performance Evaluation
Building accurate workload models using Markovian arrival processes
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Building accurate workload models using Markovian arrival processes
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Analysis of bursty workload-aware self-adaptive systems
ICPE '12 Proceedings of the 3rd ACM/SPEC International Conference on Performance Engineering
QoS and energy management with Petri nets: A self-adaptive framework
Journal of Systems and Software
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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.