Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 4: 983 - 1000

DOI: https://doi.org/10.1007/s11464-014-0411-5

RESEARCH ARTICLE

Decay properties of Markovian bulk-arrival and bulk-service queues with state-independent control

  • Lina ZHANG ,
  • Junping LI
Expand
  • School of Mathematics and Statistics, Central South University, Changsha 410075, China

Received date: 28 Mar 2014

Accepted date: 28 May 2014

Published date: 20 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

We consider decay properties regarding decay parameter and invariant measures of Markovian bulk-arrival and bulk-service queues with state-independent control. The exact value of the decay parameter, denoted by λZ, is firstly revealed. A criterion regarding λZ-recurrence and λZ-positive is obtained. The corresponding λZ-subinvariant/invariant measures and λZ-subinvariant/invariant vectors are then presented.

Key words： Decay parameter; bulk-arrival and bulk-service queues; invariant measures; invariant vectors; λC-invariant measures; λC-invariant vectors; stateindependent control

Cite this article

Lina ZHANG , Junping LI . Decay properties of Markovian bulk-arrival and bulk-service queues with state-independent control[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 983 -1000 . DOI: 10.1007/s11464-014-0411-5

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Anderson W. Continuous-Time Markov Chains: An Applications-Oriented Approach. New York: Springer-Verlag, 1991

DOI

2
Chen Anyue, Li Junping, Hou Zhenting, Wang Ng Kai. Decay properties and quasistationary distributions for stopped Markovian bulk-arrival and bulk-service queues. Queueing Syst, 2010, 66: 275-311

DOI

3
Chen Anyue, Li Junping, Ramesh N I. Uniqueness and extinction of weighted Markov branching processes. Methodol Comput Appl Probab, 2005, 7: 489-516

DOI

4
Chen Anyue, Pollett P K, Junping Li, Hanjun Zhang. Markovian bulk-arrival and bulk-service queues with state-dependent control. Queueing Syst, 2010, 64: 267-304

DOI

5
Kelly F P. Invariant measures and the generator. In: Kingman J F C, Reuter G E, eds. Probability, Statistics and Analysis. Lond Math Soc Lecture Notes Series 79. Cambridge: Cambridge University Press, 1983, 143-160

6
Kingman J F C. The exponential decay of Markov transition probability. Proc Lond Math Soc, 1963, 13: 337-358

DOI

7
Li Junping, Chen Anyue. The decay parameter and invariant measures for Markovian bulk-arrival queues with control at idle time. Methodol Comput Appl Probab, 2013, 15: 467-484

DOI

8
Nair M G, Pollett P K. On the relationship between μ-invariant measures and quasistationary distributions for continuous-time Markov chains. Adv Appl Probab, 1993, 25: 82-102

DOI

9
Pollett P K. The determination of quasi-instationary distribution directly from the transition rates of an absorbing Markov chain. Math Comput Modelling, 1995, 22: 279-287

DOI

10
Pollett P K. Quasi-stationary distributions for continuous time Markov chains when absorption is not certain. J Appl Prob, 1999, 36: 268-272

DOI

11
Van Doorn E A. Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes. Adv Appl Prob, 1991, 23: 683-700

DOI

Options
Outlines

/

〈 〉