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

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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 λ Z , is firstly revealed. A criterion regarding λ Z -recurrence and λ Z -positive is obtained. The corresponding λ Z -subinvariant/invariant measures and λ Z -subinvariant/invariant vectors are then presented.

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References

  1. Anderson W. Continuous-Time Markov Chains: An Applications-Oriented Approach. New York: Springer-Verlag, 1991

    Book  MATH  Google Scholar 

  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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  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

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  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

    Article  MATH  MathSciNet  Google Scholar 

  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

    Article  MATH  MathSciNet  Google Scholar 

  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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410075, China

    Lina Zhang & Junping Li

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  1. Lina Zhang
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  2. Junping Li
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Correspondence to Junping Li.

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Zhang, L., Li, J. Decay properties of Markovian bulk-arrival and bulk-service queues with state-independent control. Front. Math. China 9, 983–1000 (2014). https://doi.org/10.1007/s11464-014-0411-5

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

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