Journal of Mathematical Sciences

, Volume 196, Issue 1, pp 115–118 | Cite as

Loading Parameter for a Queuing System

  • I. A. Soloviev
  • A. I. Zeifman

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


Stationary Distribution Death Process Queuing System Convergence Parameter Ergodic Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Mu–Fa, “Explicit bounds of the first eigenvalue,” Sci. China, 43, 1051–1059 (2000).CrossRefGoogle 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).CrossRefMATHMathSciNetGoogle 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).CrossRefMATHGoogle 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).CrossRefMATHMathSciNetGoogle 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.Google Scholar
  6. 6.
    A. Zeifman, “Some estimates of the rate of convergence for birth and death processes,” J. Appl. Probab., 28, 268–277 (1991).CrossRefMATHMathSciNetGoogle 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).CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    B. L Granovsky and A. I. Zeifman, “Nonstationary Markovian queues,” J. Math. Sci., 99, 1415–1438 (2000).CrossRefMATHMathSciNetGoogle 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).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Vologda State Pedagogical UniversityVologda OblastRussia
  2. 2.Institute of Informatics Problems of the RASMoscowRussia
  3. 3.Institute of Socio-Economic Development of Territories of the RASVologda OblastRussia

Personalised recommendations