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Loading Parameter for a Queuing System

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

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References

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

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

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Correspondence to I. A. Soloviev.

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

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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

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  • DOI: https://doi.org/10.1007/s10958-013-1643-8

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