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Limit theorems for systems of the type M θ/G/1/b with resume level of input stream

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Abstract

We consider a queuing system of the type M θ/G/1/b in which the input stream is regulated by a certain threshold level. The asymptotic properties of the first busy period and the number of calls served during this period are studied.

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References

  1. H. Takagi, “Analysis of a finite-capacity M/G/1 queue with a resume level,” Perform. Eval., 5, No. 3, 197–203 (1985).

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  2. H. Takagi, Queueing Analysis, Vol. 2, North Holland, Amsterdam (1993).

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  3. A. M. Bratiichuk, “M θ/G/1/b system with resume level of input stream,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk., No. 1, 12–18 (2007).

  4. V. S. Korolyuk, Limit Problems for Complex Poisson Processes [in Russian], Naukova Dumka, Kiev (1975).

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  5. M. A. Evgrafov, Analytic Functions [in Russian], Nauka, Moscow (1968).

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 884–889, July, 2007.

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Bratiichuk, A.M. Limit theorems for systems of the type M θ/G/1/b with resume level of input stream. Ukr Math J 59, 976–983 (2007). https://doi.org/10.1007/s11253-007-0063-7

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  • DOI: https://doi.org/10.1007/s11253-007-0063-7

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