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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 326830, 17 pages
http://dx.doi.org/10.1155/2012/326830
Research Article

Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

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

Received 10 July 2012; Accepted 12 November 2012

Academic Editor: Joao B. R. Do Val

Copyright © 2012 Andrzej Chydzinski and Blazej Adamczyk. 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.

Abstract

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.