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Canonical form based MAP(2) fitting

Levente Bodrog, Peter Buchholz, Jan Kriege, Miklos Telek

Proc. of the 7th International Conference on Quantitative Evaluation of SysTems (QEST 2010), IEEE Computer Society, 2010.

 

Abstract

The importance of the order two Markovian arrival process (MAP(2)) comes from its compactness, serving either as arrival or service process in applications, and from the nice properties which are not available for higher order MAPs. E.g., for order two processes the acyclic MAP(2) (AMAP(2)), the MAP(2) and the order two matrix exponential process (MEP(2)) are equivalent [1]. Additionally, MAP(2) processes can be represented in a canonical form, from which closed form moments bounds are available. In this paper we investigate possible fitting methods utilizing the special nice properties of MAP(2).
We present two fitting methods. One of them partitions the exact boundaries of the MAP(2) class into bounding subsurfaces reducing the numerical inaccuracy of the optimization based moment fitting. The characterizing new feature of the other one is that it considers the distance of joint density functions of infinitely many arrivals.

 

Keywords
MAP(2), arrival process fitting

 

BibTeX
@InProceedings{BBK+10b, 
	 author = {Levente Bodrog and Peter Buchholz and Jan Kriege and Miklos Telek}, 
	 title = {{Canonical Form Based MAP(2) Fitting}}, 
	 booktitle = {Proc. of the 7th International Conference on Quantitative  
		 Evaluation of SysTems (QEST 2010)}, 
	 year = {2010}, 
	 isbn = {978-1-4244-8082-1}, 
	 doi = {10.1109/QEST.2010.22}, 
	 url = {http://doi.ieeecomputersociety.org/10.1109/QEST.2010.22}, 
	 pages = {107-116}, 
	 publisher = {IEEE Computer Society} 
 }

 

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