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A Heuristic Approach for Fitting MAPs to Moments and Joint Moments

Peter Buchholz, Jan Kriege

Proc. of the 6th International Conference on Quantitative Evaluation of SysTems (QEST 2009), IEEE Computer Society, 2009.

 

Abstract

Fitting of the parameters of a Phase Type (PH) Distribution or a Markovian Arrival Process (MAP) according to some quantities of measured data streams is still a challenge. This paper presents a new approach which computes in two steps for a set of moments and joint moments for an Acyclic PH distribution that is expanded into a MAP. In contrast to other known approaches, parameters are computed to minimize the weighted squared difference between the measured moments and the moments of the resulting PH Distribution or MAP. The proposed approach is very flexible and allows one to generate a MAP of a predefined order to approximate a given set of moments and joint moments. It is shown that the approximation is often sufficiently accurate even with MAPs of a moderate size. However, we also show that the practical applicability of the approach is limited since the exact determination of higher order moments from traces requires an extremely high effort.

 

Keywords
Acyclic Phase Type Distributions, Markovian Arrival Processes, Moments, Fitting Procedures

 

BibTeX
@InProceedings{BKr09, 
	 author = {Peter Buchholz and Jan Kriege}, 
	 title = {{A Heuristic Approach for Fitting MAPs to Moments and Joint Moments}}, 
	 booktitle = {Proc. of the 6th International Conference on Quantitative  
		 Evaluation of SysTems (QEST 2009)}, 
	 year = {2009}, 
	 isbn = {978-0-7695-3808-2}, 
	 doi = {10.1109/QEST.2009.36}, 
	 url = {http://doi.ieeecomputersociety.org/10.1109/QEST.2009.36}, 
	 pages = {53-62}, 
	 publisher = {IEEE Computer Society}, 
	 address = {Los Alamitos, CA, USA} 
 }

 

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