Breuer, Lothar (2001) The Periodic BMAP/PH/c Queue. Queueing Systems, 38 (1). pp. 67-76. ISSN 0257-0130. (The full text of this publication is not available from this repository)
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In queueing theory, most models are based on time-homogeneous arrival processes and service time distributions. However, in communication 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. Furthermore, 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/M-t/c queue with periodically varying service rates by the same method.
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Lothar Breuer|
|Date Deposited:||14 Sep 2008 08:36|
|Last Modified:||14 Jan 2010 14:14|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/4036 (The current URI for this page, for reference purposes)|