Matrix-geometric solutions of M/G/1-type Markov chains: A unifying generalized state-space approach

Simple item page
dc.citation.epage639en_US
dc.citation.issueNumber5en_US
dc.citation.spage626en_US
dc.citation.volumeNumber16en_US
dc.contributor.authorAkar, N.en_US
dc.contributor.authorOǧuz, N.C.en_US
dc.contributor.authorSohraby, K.en_US
dc.date.accessioned2016-02-08T10:45:03Z
dc.date.available2016-02-08T10:45:03Z
dc.date.issued1998en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractIn this paper, we present an algorithmic approach to find the stationary probability distribution of M/G/1-type Markov chains which arise frequently in performance analysis of computer and communication networ ks. The approach unifies finite- and infinite-level Markov chains of this type through a generalized state-space representation for the probability generating function of the stationary solution. When the underlying probability generating matrices are rational, the solution vector for level k, x k, is shown to be in the matrix-geometric form x k+1 = gF k H, k ≥ 0, for the infinite-level case, whereas it takes the modified form x k+1 = g 1F 1 kH 1 + g 2F 2 K-k-1 H 2, 0 ≤ k < K, for the finite-level case. The matrix parameters in the above two expressions can be obtained by decomposing the generalized system into forward and backward subsystems, or, equivalently, by finding bases for certain generalized invariant subspaces of a regular pencil λE - A. We note that the computation of such bases can efficiently be carried out using advanced numerical linear algebra techniques including matrix-sign function iterations with quadratic convergence rates or ordered generalized Schur decomposition. The simplicity of the matrix-geometric form of the solution allows one to obtain various performance measures of interest easily, e.g., overflow probabilities and the moments of the level distribution, which is a significant advantage over conventional recursive methods.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T10:45:03Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 1998en
dc.identifier.doi10.1109/49.700901en_US
dc.identifier.issn0733-8716
dc.identifier.urihttp://hdl.handle.net/11693/25455
dc.language.isoEnglishen_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/49.700901en_US
dc.source.titleIEEE Journal on Selected Areas in Communicationsen_US
dc.subjectATM multiplexer analysisen_US
dc.subjectGeneralized difference equationsen_US
dc.subjectGeneralized invariant subspacesen_US
dc.subjectGeneralized Schur decompositionen_US
dc.subjectM/G/1-type Markov chainsen_US
dc.subjectMatrix-sign functionen_US
dc.subjectPolynomial matrix fractional descriptionsen_US
dc.subjectAsynchronous transfer modeen_US
dc.subjectDifference equationsen_US
dc.subjectIterative methodsen_US
dc.subjectMarkov processesen_US
dc.subjectMatrix algebraen_US
dc.subjectMultiplexing equipmenten_US
dc.subjectPolynomialsen_US
dc.subjectState space methodsen_US
dc.subjectGeneralized Schur decompositionen_US
dc.subjectMatrix geometric solutionsen_US
dc.subjectMatrix sign functionen_US
dc.subjectTelecommunication trafficen_US
dc.titleMatrix-geometric solutions of M/G/1-type Markov chains: A unifying generalized state-space approachen_US
dc.typeArticleen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Matrix.pdf
Size:
598.09 KB
Format:
Adobe Portable Document Format
Description:
Full printable version
Download

Collections

Department of Electrical and Electronics Engineering