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

• Autorzy: András Mészáros , János Papp , Miklós Telek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fitting traffic traces; discrete phase type distribution; discrete Markov arrival process; canonical representation

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2014
• Tom: 24
• Numer: 3
• Strony: 453-470

Daty

wydano

2014

otrzymano

2013-08-20

poprawiono

2014-02-10

poprawiono

2014-02-26

Twórcy

autor

András Mészáros

• Department of Networked Systems and Services, Budapest University of Technology and Economics, Magyar tudósok krt 2, 1117 Budapest, Hungary
• Inter-University Center for Telecommunications and Informatics, Kassai út 26, 4028 Debrecen, Hungary

autor

János Papp

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

autor

Miklós Telek

• 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

Bibliografia

• Alfa, A. (2002). Discrete time queues and matrix-analytic methods, Top 10(2): 147-185.
• Bodrog, L., Heindl, A., Horváth, G. and Telek, M. (2008). A Markovian canonical form of second-order matrix-exponential processes, European Journal of Operation Research 190: 459-477.
• Horváth, G. and Telek, M. (2007). A canonical representation of order 3 phase type distributions, in K. Volter (Ed.), Formal Methods and Stochastic Models for Performance Evaluation, Springer, Berlin/Heidelberg, pp. 48-62.
• Horváth, G. and Telek, M. (2009). On the canonical representation of phase type distributions, Performance Evaluation 66(8): 396-409.
• Lakatos, L., Szeidl, L. and Telek, M. (2013). Introduction to Queueing Systems with Telecommunication Applications, Springer, New York, NY.
• Neuts, M. (1981). Matrix Geometric Solutions in Stochastic Models, Johns Hopkins University Press, Baltimore, MD.
• Telek, M. and Heindl, A. (2002). Matching moments for acyclic discrete and continuous phase-type distributions of second order, International Journal of Simulation Systems, Science & Technology 3(3-4): 47-57.
• Telek, M. and Horváth, G. (2007). A minimal representation of Markov arrival processes and a moments matching method, Performance Evaluation 64(9-12): 1153-1168.

Identyfikatory

DOI

10.2478/amcs-2014-0034