Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Authors:
Soohan Ahn;Andrei L. Badescu;V. Ramaswami
Affiliations:
Department of Statistics, The University of Seoul, Seoul, South Korea 130-743;Department of Statistics, University of Toronto, Toronto, Canada M5S 3G3;AT&T Labs-Research, Florham Park, USA 07932
Venue:
Queueing Systems: Theory and Applications
Year:
2007

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Abstract

Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.