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Long range dependence of point processes, with queueing examples

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  • Daley, D.J.
  • Vesilo, Rein

Abstract

Possible definitions of the long range dependence (LRD) of a stationary point process are discussed. Examples from the standard queueing literature are considered and shown to be amenable to yielding processes with long range count dependence. In particular the effect of the single-server queueing operator, whereby one point process is transformed into another via the mechanism of a simple queue, is examined for possible long range dependence of both the counting and interval properties of the output process. For an infinite server queue, the output is long range count dependent if and only if the input is long range count dependent.

Suggested Citation

  • Daley, D.J. & Vesilo, Rein, 1997. "Long range dependence of point processes, with queueing examples," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 265-282, October.
    • Handle: RePEc:eee:spapps:v:70:y:1997:i:2:p:265-282
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    References listed on IDEAS

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    1. Daley, D. J., 1975. "Further second-order properties of certain single-server queueing systems," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 185-191, April.
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    Cited by:

    1. de Coninck, Joël & Dunlop, François & Huillet, Thierry, 2008. "On the correlation structure of some random point processes on the line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 725-744.
    2. Hautphenne, Sophie & Kerner, Yoav & Nazarathy, Yoni & Taylor, Peter, 2015. "The intercept term of the asymptotic variance curve for some queueing output processes," European Journal of Operational Research, Elsevier, vol. 242(2), pages 455-464.
    3. R. Jiang, 2022. "Two approximations of renewal function for any arbitrary lifetime distribution," Annals of Operations Research, Springer, vol. 311(1), pages 151-165, April.
    4. Jiang, R., 2020. "A novel two-fold sectional approximation of renewal function and its applications," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    5. Rohit Deo & Mengchen Hsieh & Clifford Hurvich, 2005. "Tracing the Source of Long Memory in Volatility," Econometrics 0501005, University Library of Munich, Germany.

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    1. Hautphenne, Sophie & Kerner, Yoav & Nazarathy, Yoni & Taylor, Peter, 2015. "The intercept term of the asymptotic variance curve for some queueing output processes," European Journal of Operational Research, Elsevier, vol. 242(2), pages 455-464.

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