A comprehensive study on the queue-size distribution in a finite-buffer system with a general independent input flow

Wojciech M. Kempa

doi:10.1016/j.peva.2016.11.002

A comprehensive study on the queue-size distribution in a finite-buffer system with a general independent input flow

Wojciech M. Kempa

Katedra Metod Matematycznych w Technice i Informatyce (RMS/RMS3)

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

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Abstrakt

A finite-buffer GI/M/1/N− type queueing model is considered. The explicit formula for the Laplace transform of the transient queue-size distribution, conditioned by the number of packets present in the system at the starting time, is derived. The shape of the formula allows for finding the stationary distribution by applying the key renewal theorem. Moreover, the convergence rate of the transient queue-size distribution to the stationary one is determined with the constant value given explicitly. Numerical example is attached as well.

Język oryginału	angielski
Strony (od–do)	1-15
Liczba stron	15
Czasopismo	Performance Evaluation
Tom	108
Identyfikatory DOI	https://doi.org/10.1016/j.peva.2016.11.002
Status publikacji	Opublikowano - 1 lut 2017

Obszary tematyczne ASJC Scopus

Oprogramowanie
Modelowanie i symulacja
Sprzęt i architektura
Sieci komputerowe i komunikacja

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10.1016/j.peva.2016.11.002

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Cytowanie

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abstract = "A finite-buffer GI/M/1/N− type queueing model is considered. The explicit formula for the Laplace transform of the transient queue-size distribution, conditioned by the number of packets present in the system at the starting time, is derived. The shape of the formula allows for finding the stationary distribution by applying the key renewal theorem. Moreover, the convergence rate of the transient queue-size distribution to the stationary one is determined with the constant value given explicitly. Numerical example is attached as well.",

keywords = "Convergence rate, Finite buffer, Queue-size distribution, Renewal theory",

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N2 - A finite-buffer GI/M/1/N− type queueing model is considered. The explicit formula for the Laplace transform of the transient queue-size distribution, conditioned by the number of packets present in the system at the starting time, is derived. The shape of the formula allows for finding the stationary distribution by applying the key renewal theorem. Moreover, the convergence rate of the transient queue-size distribution to the stationary one is determined with the constant value given explicitly. Numerical example is attached as well.

AB - A finite-buffer GI/M/1/N− type queueing model is considered. The explicit formula for the Laplace transform of the transient queue-size distribution, conditioned by the number of packets present in the system at the starting time, is derived. The shape of the formula allows for finding the stationary distribution by applying the key renewal theorem. Moreover, the convergence rate of the transient queue-size distribution to the stationary one is determined with the constant value given explicitly. Numerical example is attached as well.

KW - Convergence rate

KW - Finite buffer

KW - Queue-size distribution

KW - Renewal theory

UR - https://www.scopus.com/pages/publications/85007391419

U2 - 10.1016/j.peva.2016.11.002

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JO - Performance Evaluation

JF - Performance Evaluation

ER -

A comprehensive study on the queue-size distribution in a finite-buffer system with a general independent input flow

Abstrakt

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