Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1099.60061
Li, Quan-Lin; Zhao, Yiqiang Q.
Light-tailed asymptotics of the stationary probability vectors of Markov chains of GI/G/1 type. (English)
[J] Adv. Appl. Probab. 37, No. 4, 1075-1093 (2005). ISSN 0001-8678

The paper deals with the light-tailed asymptotic behavior of stationary probability vectors of block-structured Markov chains. It presents a novel approach to evaluating the light-tailed asymptotics by means of the RG-factorization of both the repeating blocks and the Wiener-Hopf equations for the boundary blocks of the transition probability matrix, the RG-factorization plays a role similar to that played by the Wiener-Hopf factorization in analyzing waiting times. The stationary probability vector is partitioned into vectors $(\pi _0,\pi _1,\pi _2,\ldots )$, $\{\pi _k\}$ are expressed in terms of the R-measure and, finally, in terms of the blocks in the transition probability matrix of GI/G/1 type. This expression can be used to show that $\{\pi _k\}$ is light-tailed under certain condition. The paper explicitly presents the tail-asymptotics of $\{\pi _k\}$. There are defined three classes of sequences of nonnegative matrices, two of them exhibit light-tailed asymptotics, the third heavy-tailed one. The classification of $\{\pi _k\}$ is discussed in terms of the classification of the repeating row and the boundary row.
[Laszlo Lakatos (Budapest)]

MSC 2000:: *60K25 Queueing theory
60K15 Markov renewal processes
60J22 Computational methods in Markov chains
90B22 Queues and service

Keywords: asymptotic analysis

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]