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.
Similar content being viewed by others
References
H. Takagi, “Analysis of a finite-capacity M/G/1 queue with a resume level,” Perform. Eval., 5, No. 3, 197–203 (1985).
H. Takagi, Queueing Analysis, Vol. 2, North Holland, Amsterdam (1993).
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).
V. S. Korolyuk, Limit Problems for Complex Poisson Processes [in Russian], Naukova Dumka, Kiev (1975).
M. A. Evgrafov, Analytic Functions [in Russian], Nauka, Moscow (1968).
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 884–889, July, 2007.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11253-007-0063-7