The periodic BMAP/PH/c queue

The periodic BMAP/PH/c queue

0.00 Avg rating0 Votes
Article ID: iaor20041269
Country: Netherlands
Volume: 38
Issue: 1
Start Page Number: 67
End Page Number: 76
Publication Date: May 2001
Journal: Queueing Systems
Authors:
Keywords: GI/G/c queues
Abstract:

In queueing theory, most models are based on time-homogeneous arrival processes and service time distributions. However, in communications networks arrival rates and/or the service capacity usually vary periodically in time. In order to reflect this property accurately, one needs to examine periodic rather than homogeneous queues. In the present paper, the periodic BMAP/PH/c queue is analyzed. This queue has a periodic BMAP arrival process, which is defined in this paper, and phase-type service time distributions. As a Markovian queue, it can be analysed like an (inhomogeneous) Markov jump process. The transient distribution is derived by solving the Kolmogorov forward equations. Futhermore, a stability condition in terms of arrival and service rates is proven and for the case of stability, the asymptotic distribution is given explicitly. This turns out to be a periodic family of probability distributions. It is sketched how to analyze the periodic BMAP/Mt /c queue with periodically varying service rates by the same method.

Reviews

Required fields are marked *. Your email address will not be published.