zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Heavy-tailed asymptotics of stationary probability vectors of Markov chains of GI/G/1 type. (English) Zbl 1076.60081
The paper presents a novel approach to analyze the heavy-tailed asymptotics of the stationary probability vector of a Markov chain of GI/G/1 type. The use of the R-measure, the RG-factorization of the repeating matrix sequence, and a Wiener-Hopf equation are the keys to this approach. The main contributions are threefold. First, some properties of heavy-tailed sequences of nonnegative scalars are extended to matrix form for sequences of nonnegative matrices. Second, the paper provides a necessary and sufficient condition under which the stationary probability vector is heavy-tailed. Third, the long-tailed asymptotics of the R-measure is derived in terms of the RG-factorization of the repeating matrix sequence and a Wiener-Hopf equation for the boundary matrix sequence.
MSC:
60K25Queueing theory
60K15Markov renewal processes
60J22Computational methods in Markov chains
90B22Queues and service (optimization)