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The rate of convergence in limit theorems for service systems with finite queue capacity

Published online by Cambridge University Press:  14 July 2016

Joseph Tomko
Joseph Tomko*
Affiliation:
Computer Centre of Hungarian Academy of Sciences, Budapest
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Abstract

The paper deals with the asymptotic analysis of waiting time distribution for service systems with finite queue capacity. First an M/M/m system is considered and the rate of approximation is given. Then the case of the M/G/1 system is studied for traffic intensity ρ > 1. In the last section a condition is given under which an estimate can be derived for the remainder term in central limit theorems for randomly stopped sums.

Keywords

QUEUEING THEORYSERVICE SYSTEM WITH FINITE CAPACITYCENTRAL LIMIT THEOREMRANDOMLY STOPPED SUMSRATE OF CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 87 - 102
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Gnedenko, B. V. and Kovalenko, I. N. (1966) (Eng. Transl. 1968) Introduction to Queuing Theory. Israel Program for Scientific Translations, Jerusalem 1968.Google Scholar
[2] Keilson, J. (1966) The ergodic queue length distribution for queueing systems with finite capacity. J. R. Statist. Soc. B28, 190–201.Google Scholar
[3] Takács, L. (1957) On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hung. 8, 169–191.Google Scholar
[4] Rényi, A. (1957) On the asymptotic distribution of a random number of independent random variables. Acta Math. Acad. Sci. Hung. 8, 193–199.Google Scholar
[5] Tomko, J. (1967) Véges sorkapacitású egykiszolgálós várakozási idö-problémáról. MTA Számitástechn. Közp. Közl. 3.Google Scholar
[6] Tomko, J. (1971) On estimation of the residual in the central limit theorem for sums of random number of summands. Teor. Veroyat. Primen. 16, 164–172.Google Scholar