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Mathematical Problems in EngineeringVolume 2012 2012, Article ID 831956, 18 pages

Research ArticleInstitute of Informatics, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Received 24 June 2011; Revised 21 October 2011; Accepted 21 October 2011

Academic Editor: Angelo Luongo

Copyright © 2012 Andrzej Chydzinski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We deal with finite-buffer queueing systems fed by a Markovian pointprocess. This class includes the queues of type M-G-1-N -G-1-N, PH-G-1-N,MMPP-G-1-N, MAP-G-1-N, and BMAP-G-1-N and is commonly used in the performance evaluation of network traffic buffering processes. Typically, such queueingsystems are studied in the stationary regime using matrix-analytic methods connected with M-G-1-type Markov processes. Herein, another method for findingtransient and stationary characteristics of these queues is presented. The approachis based on finding a closed-form formula for the Laplace transform of the time-dependent performance measure of interest. The method can be used for findingall basic characteristics like queue size distribution, workload distribution, loss ratio, time to buffer overflow, and so forth. To demonstrate this, several examples for differentcombinations of arrival processes and characteristics are presented. In addition, themost complex results are illustrated via numerical calculations based on an IP trafficparameterization.

Autor: Andrzej Chydzinski

Fuente: https://www.hindawi.com/


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