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Light tail asymptotics in multidimensional reflecting processes for queueing networks

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  • Masakiyo Miyazawa

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  • Masakiyo Miyazawa, 2011. "Light tail asymptotics in multidimensional reflecting processes for queueing networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 233-299, December.
    • Handle: RePEc:spr:topjnl:v:19:y:2011:i:2:p:233-299
    DOI: 10.1007/s11750-011-0179-7
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. David Gamarnik, 2002. "On Deciding Stability of Constrained Homogeneous Random Walks and Queueing Systems," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 272-293, May.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    4. P. Lieshout & M. Mandjes, 2007. "Tandem Brownian queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 275-298, October.
    5. Anatolii A. Puhalskii & Alexander A. Vladimirov, 2007. "A Large Deviation Principle for Join the Shortest Queue," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 700-710, August.
    6. Alsmeyer, Gerold, 1994. "On the Markov renewal theorem," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 37-56, March.
    7. Yiqiang Q. Zhao & Wei Li & W. John Braun, 2003. "Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 35-58, March.
    8. Jiashan Tang & Yiqiang Zhao, 2008. "Stationary tail asymptotics of a tandem queue with feedback," Annals of Operations Research, Springer, vol. 160(1), pages 173-189, April.
    9. Dupuis, Paul & Ramanan, Kavita, 2002. "A time-reversed representation for the tail probabilities of stationary reflected Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 253-287, April.
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    Citations

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    Cited by:

    1. Toshihisa Ozawa, 2022. "Tail asymptotics in any direction of the stationary distribution in a two-dimensional discrete-time QBD process," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 227-267, October.
    2. Ioannis Dimitriou, 2021. "On partially homogeneous nearest-neighbour random walks in the quarter plane and their application in the analysis of two-dimensional queues with limited state-dependency," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 95-143, June.
    3. Yanting Chen & Richard J. Boucherie & Jasper Goseling, 2016. "Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 21-48, October.
    4. Yanting Chen & Richard J. Boucherie & Jasper Goseling, 2020. "Necessary conditions for the compensation approach for a random walk in the quarter-plane," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 257-277, April.
    5. Yiqiang Q. Zhao, 2022. "The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 95-131, February.
    6. Mihail Bazhba & Chang-Han Rhee & Bert Zwart, 2022. "Large deviations for stochastic fluid networks with Weibullian tails," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 25-52, October.
    7. Kamil Demirberk Ünlü & Ali Devin Sezer, 2020. "Excessive backlog probabilities of two parallel queues," Annals of Operations Research, Springer, vol. 293(1), pages 141-174, October.
    8. Ioannis Dimitriou, 2022. "Stationary analysis of certain Markov-modulated reflected random walks in the quarter plane," Annals of Operations Research, Springer, vol. 310(2), pages 355-387, March.
    9. Toshihisa Ozawa & Masahiro Kobayashi, 2018. "Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 351-403, December.
    10. Toshihisa Ozawa, 2021. "Asymptotic properties of the occupation measure in a multidimensional skip-free Markov-modulated random walk," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 125-161, February.

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