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Title: Study of Queuing Systems with a Generalized Departure Process
Authors: Mirtchev, Seferin
Statev, Stanimir
Keywords: Loss and Delay System
Queueing Analyses
State Dependent Service Rate
Birth and Death Process
Peaked and Smooth Traffic
Issue Date: 2008
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 2, No 1, (2008), 57p-72p
Abstract: This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based on birth and death processes and state-dependent service rates. We consider the system M/M(g)/n/0 and M/M(g)/1/k (in Kendal notation) with a generalized departure process Mg. The output intensity depends nonlinearly on the system state with a defined parameter: “peaked factor p”. We obtain the state probabilities of the system using the general solution of the birth and death processes. The influence of the peaked factor on the state probability distribution, the congestion probability and the mean system time are studied. It is shown that the state-dependent service rates changes significantly the characteristics of the queueing systems. The advantages of simplicity and uniformity in representing both peaked and smooth behaviour make this queue attractive in network analysis and synthesis.
Description: This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.
ISSN: 1312-6555
Appears in Collections:Volume 2 Number 1

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