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Asymptotic independence of regenerative processes with a special dependence structure

Author

Listed:
  • Royi Jacobovic

    (The Hebrew University of Jerusalem)

  • Offer Kella

    (The Hebrew University of Jerusalem)

Abstract

We identify some conditions under which regenerative processes with a certain dependence structure among them are asymptotically independent. The result is applied to various models, in particular independent Lévy processes with dependent secondary jumps at the origin (for example, workloads of parallel M/G/1 queues with server vacations), the asymptotic performance of systems with multiple correlated sources that generate real-time status updates measured by the limiting probability of an updated system, and asymptotic results for clearing processes with dependent arrivals of clearings. Finally, the asymptotic distribution of the classic Jackson network is discussed as yet another example.

Suggested Citation

  • Royi Jacobovic & Offer Kella, 2019. "Asymptotic independence of regenerative processes with a special dependence structure," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 139-152, October.
    • Handle: RePEc:spr:queues:v:93:y:2019:i:1:d:10.1007_s11134-019-09606-1
    DOI: 10.1007/s11134-019-09606-1
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    References listed on IDEAS

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    1. Ward Whitt, 1981. "The Stationary Distribution of a Stochastic Clearing Process," Operations Research, INFORMS, vol. 29(2), pages 294-308, April.
    2. Shaler Stidham, 1977. "Cost Models for Stochastic Clearing Systems," Operations Research, INFORMS, vol. 25(1), pages 100-127, February.
    3. Serfozo, Richard & Stidham, Shaler, 1978. "Semi-stationary clearing processes," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 165-178, January.
    4. Thorisson, Hermann, 1992. "Construction of a stationary regenerative process," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 237-253, September.
    5. Stidham, Shaler, 1974. "Stochastic clearing systems," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 85-113, January.
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    Cited by:

    1. Karamzadeh, M. & Soltani, A.R. & Mardani-Fard, H.A., 2020. "On a class of spatial renewal processes: Renewal processes synchronization probabilities," Statistics & Probability Letters, Elsevier, vol. 158(C).
    2. Jacobovic, Royi & Kella, Offer, 2020. "Minimizing a stochastic convex function subject to stochastic constraints and some applications," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 7004-7018.

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