On the Convergence of a Multidimensional Workload in a Service System to a Stable Process

  • 2 Accesses

A service system model introduced by I. Kaj and M. S. Taqqu is considered. We prove a limit theorem on the convergence of finite-dimensional distributions of the integral workload process with a multidimensional resource to the corresponding distributions of a multidimensional stable process.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.


  1. 1.

    I. Kaj and M. S. Taqqu, “Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach,” in: In and Out of Equilibrium. II, Progress in Probability, 60, Birkhäuser, Basel (2008), pp. 383–427.

  2. 2.

    M. A. Lifshits, Random Processes – From Theory to Practice [in Russian], St.Petersburg (2016).

  3. 3.

    H. Biermé, A. Estrade, and I. Kaj, “Self-similar random fields and rescaled random balls models,” J. Theor. Probab., 23, 1110–1141 (2010).

  4. 4.

    J.-C. Breton and C. Dombry, “Self-similar random fields and rescaled random balls models,” Stoch. Proc. Appl., 119, 3633–3652 (2009).

  5. 5.

    I. Kaj, L. Leskelä, I. Norros, and V. Schmidt, “Scaling limits for random fields with longrange dependence,” Ann. Probab., 35, 528–550 (2007).

  6. 6.

    A. N. Shiryaev, Probability [in Russian], Moscow (1980).

  7. 7.

    A. V. Skorokhod, Random Processes with Independent Increments [in Russian], Moscow (1964).

  8. 8.

    A. V. Skorokhod, Studies in the Theory of Random Processes [in Russian], Kiev (1961).

  9. 9.

    B. V. Gnedenko, A Course of Probability Theory [in Russian], Moscow (2004).

  10. 10.

    I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Sequences of Random Variables [in Russian], Moscow (1965).

Download references

Author information

Correspondence to E. S. Garai.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 96–108.

Translated by S. Yu. Pilyugin.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Garai, E.S. On the Convergence of a Multidimensional Workload in a Service System to a Stable Process. J Math Sci 244, 762–770 (2020) doi:10.1007/s10958-020-04649-9

Download citation