<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Recent developments of matrix analytic methods make phase type distributions (PHs) and Markov Arrival Processes (MAPs) promising stochastic model candidates for capturing traffic trace behaviour and for efficient usage in queueing analysis. After introducing basics of these sets of stochastic models, the paper discusses the following subjects in detail: (i) PHs and MAPs have different representations. For efficient use of these models, sparse (defined by a minimal number of parameters) and unique representations of discrete time PHs and MAPs are needed, which are commonly referred to as canonical representations. The paper presents new results on the canonical representation of discrete PHs and MAPs. (ii) The canonical representation allows a direct mapping between experimental moments and the stochastic models, referred to as moment matching. Explicit procedures are provided for this mapping. (iii) Moment matching is not always the best way to model the behavior of traffic traces. Model fitting based on appropriately chosen distance measures might result in better performing stochastic models. We also demonstrate the efficiency of fitting procedures with experimental results</p></abstract>

Recent developments of matrix analytic methods make phase type distributions (PHs) and Markov Arrival Processes (MAPs) promising stochastic model candidates for capturing traffic trace behaviour and for efficient usage in queueing analysis. After introducing basics of these sets of stochastic models, the paper discusses the following subjects in detail: (i) PHs and MAPs have different representations. For efficient use of these models, sparse (defined by a minimal number of parameters) and unique representations of discrete time PHs and MAPs are needed, which are commonly referred to as canonical representations. The paper presents new results on the canonical representation of discrete PHs and MAPs. (ii) The canonical representation allows a direct mapping between experimental moments and the stochastic models, referred to as moment matching. Explicit procedures are provided for this mapping. (iii) Moment matching is not always the best way to model the behavior of traffic traces. Model fitting based on appropriately chosen distance measures might result in better performing stochastic models. We also demonstrate the efficiency of fitting procedures with experimental results

Fitting traffic traces with discrete canonical phase type distributions and Markov arrival processes

Department of Networked Systems and Services Budapest University of Technology and Economics, Magyar tudósok krt 2, 1117 Budapest, Hungary

MTA-BME Information Systems Research Group Magyar tudósok krt. 2, 1117 Budapest, Hungary

Inter-University Center for Telecommunications and Informatics Kassai ´ut 26, 4028 Debrecen, Hungary

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Recent developments of matrix analytic methods make phase type distributions (PHs) and Markov Arrival Processes (MAPs) promising stochastic model candidates...

Fitting traffic traces with discrete canonical phase type distributions and Markov arrival processes

Publié en ligne: 25 sept. 2014

Pages: 453 - 470

Reçu: 20 août 2013

DOI: https://doi.org/10.2478/amcs-2014-0034

Mots clés
fitting traffic traces, discrete phase type distribution, discrete Markov arrival process, canonical representation

© by András Meszáros

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fitting traffic traces with discrete canonical phase type distributions and Markov arrival processes

Publié en ligne: 25 sept. 2014

Pages: 453 - 470

Reçu: 20 août 2013

DOI: https://doi.org/10.2478/amcs-2014-0034

Mots clésfitting traffic traces, discrete phase type distribution, discrete Markov arrival process, canonical representation

© by András Meszáros

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
fitting traffic traces, discrete phase type distribution, discrete Markov arrival process, canonical representation