Loading Parameter for a Queuing System

In this paper, an accurate bound is obtained of a loading parameter for the queuing system M/M/N.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    C. Mu–Fa, “Explicit bounds of the first eigenvalue,” Sci. China, 43, 1051–1059 (2000).

    Article  Google Scholar 

  2. 2.

    P. Coolen–Schrijner and E. van Doorn, “On the convergence to stationarity of birth-death processes,” J. Appl. Probab., 38, 696–706 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  3. 3.

    E. van Doorn, “Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process,” Adv. Appl. Probab., 17, 514–530 (1985).

    Article  MATH  Google Scholar 

  4. 4.

    N. V. Kartashov, “The determination of the spectral ergodicity index for birth-and-death processes,” Ukr. Math. J., 52, 889–897 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  5. 5.

    A. I. Zeifman, “Quality properties of non-homogeneous birth-and-death processes,” in: Stability Problems of Stochastic Models [in Russian], Institute for Systems Studies, Moscow (1988), pp. 32–40.

  6. 6.

    A. Zeifman, “Some estimates of the rate of convergence for birth and death processes,” J. Appl. Probab., 28, 268–277 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  7. 7.

    A. Zeifman, “Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes,” Stoch. Process. Appl., 59, 157–173 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  8. 8.

    B. L Granovsky and A. I. Zeifman, “Nonstationary Markovian queues,” J. Math. Sci., 99, 1415–1438 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  9. 9.

    Ju.L. Dalec’kii and M.G. Krein, Stability of Solutions of Differential Equations in Banach Space, American Mathematical Society, Providence (1974).

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to I. A. Soloviev.

Additional information

Proceedings of the XXVI International Seminar on Stability Problems for Stochastic Models, Sovata-Bai, Romania, August 27 – September 2, 2006.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Soloviev, I.A., Zeifman, A.I. Loading Parameter for a Queuing System. J Math Sci 196, 115–118 (2014). https://doi.org/10.1007/s10958-013-1643-8

Download citation

Keywords

  • Stationary Distribution
  • Death Process
  • Queuing System
  • Convergence Parameter
  • Ergodic Process