Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 401365, 31 pages
Research Article

The 𝑁 × 𝐷 -BMAP/G/1 Queueing Model: Queue Contents and Delay Analysis

Department of Telecommunications and Information Processing (IR07), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium

Received 20 May 2011; Accepted 1 July 2011

Academic Editor: Alexander Pogromsky

Copyright © 2011 Bart Steyaert et al. 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 consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression for their steady-state probability generating function, and from these results, we derive closed-form expressions for key performance measures such as their mean value, variance, and tail distribution. A lot of emphasis is put on finding closed-form expressions for these quantities that reduce all numerical calculations to an absolute minimum.