ON THE ERGODICITY OF A CLASS OF LEVEL-DEPENDENT QUASI-BIRTH-AND-DEATH PROCESSES

We examine necessary and sufficient conditions tor recurrence and positive recurrence of a class of irreducible, level-dependent quasi-birth-and-death (LDQBD) processes with a block tridiagonal structure that exhibits asymptotic convergence in the rows as the level tends to infinity. These condition...

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Bibliographic Details
Published inAdvances in applied probability Vol. 51; no. 4; pp. 1109 - 1128
Main Authors CORDEIRO, JAMES D., KHAROUFEH, JEFFREY P., OXLEY, MARK E.
Format Journal Article
LanguageEnglish
Published Sheffield Applied Probability Trust 01.12.2019
Cambridge University Press
Subjects
Algorithms
Applied mathematics
Customer services
Death
Drift
Markov analysis
Probability
Queuing theory
Stochastic models
United States > US
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Summary:We examine necessary and sufficient conditions tor recurrence and positive recurrence of a class of irreducible, level-dependent quasi-birth-and-death (LDQBD) processes with a block tridiagonal structure that exhibits asymptotic convergence in the rows as the level tends to infinity. These conditions are obtained by exploiting a multidimensional Lyapunov drift approach, along with the theory of generalized Markov group inverses. Additionally, we highlight analogies to well-known average drift results for level-independent quasi-birth-and-death (QBD) processes.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2019.43