Queue response to input correlation functions: continuous spectral analysis
IEEE/ACM Transactions on Networking (TON)
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling
An EM algorithm for estimation in Markov-modulated Poisson processes
Computational Statistics & Data Analysis
On the relevance of long-range dependence in network traffic
Conference proceedings on Applications, technologies, architectures, and protocols for computer communications
On variations of queue response for inputs with the same mean and autocorrelation function
IEEE/ACM Transactions on Networking (TON)
Connection-wise end-to-end performance analysis of queuing networks with MMPP inputs
Performance Evaluation
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
Fast Algorithms for Measurement-Based Traffic Modeling
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
Modeling multiple IP traffic streams with rate limits
IEEE/ACM Transactions on Networking (TON)
An EM-based technique for approximating long-tailed data sets with PH distributions
Performance Evaluation - Internet performance symposium (IPS 2002)
Queueing Systems: Theory and Applications
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
A minimal representation of Markov arrival processes and a moments matching method
Performance Evaluation
KPC-Toolbox: Simple Yet Effective Trace Fitting Using Markovian Arrival Processes
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
A canonical representation of order 3 phase type distributions
EPEW'07 Proceedings of the 4th European performance engineering conference on Formal methods and stochastic models for performance evaluation
A multifractal wavelet model with application to network traffic
IEEE Transactions on Information Theory
IEEE Journal on Selected Areas in Communications
Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data
IEEE Journal on Selected Areas in Communications
KPC-Toolbox: Best recipes for automatic trace fitting using Markovian Arrival Processes
Performance Evaluation
Multi-class Markovian arrival processes and their parameter fitting
Performance Evaluation
Correlated phase-type distributed random numbers as input models for simulations
Performance Evaluation
Bandwidth allocation under end-to-end percentile delay bounds
International Journal of Network Management
Retrial queuing system with Markovian arrival flow and phase-type service time distribution
Computers and Industrial Engineering
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We propose a trace fitting algorithm for Markovian Arrival Processes (MAPs) that can capture statistics of any order of interarrival times between measured events. By studying real traffic and workload traces often used in performance evaluation studies, we show that matching higher order statistical properties, in addition to first and second order descriptors, results in increased queueing prediction accuracy with respect to algorithms that only match the mean, the coefficient of variation, and the autocorrelations of the trace. This result supports the approach of modeling traces by the interarrival time process instead of the counting process that is more frequently used in the literature. We proceed by first characterizing the general properties of MAPs using a spectral approach. Based on this result, we show how different MAPs can be combined together using Kronecker products to define a larger MAP with predefined properties of interarrival times. We then devise an algorithm that is based on this Kronecker composition and can accurately fit data traces. This MAP fitting algorithm uses nonlinear optimization that can be customized to fit an arbitrary number of moments and to meet the desired cost-accuracy tradeoff. Numerical results of the fitting algorithm on real data, such as the Bellcore Aug89 trace and a Seagate disk drive trace, indicate that the proposed fitting technique achieves increased prediction accuracy with respect to other state-of-the-art fitting methods.