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University of Ulm, Faculty of Mathematics and Economics
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Asymptotics of Palm-stationary Buffer Content Distributions
in Fluid Flow Queues
Department of Stochastics
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General Information
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| Author: |
Tomasz Rolski and Sabine Schlegel and Volker Schmidt |
| To appear in: |
Advances in Applied Probability, March 1999 |
| Contact: |
schlegel@mathematik.uni-ulm.de |
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Abstract
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We study a fluid flow queueing system with m independent sources alternating between silence and activity periods. The distribution function of the activity periods of one source is supposed to be intermediate regular varying. We show that
the distribution of the net increment of the buffer during an aggregate activity period (i.e. at least one source is active) is asymptotically tail-equivalent to the distribution of the net input during a single activity period with intermediate regular varying distribution function. In this way, we arrive at an asymptotical representation of the Palm-stationary tail-function of the buffer content at the beginning of aggregate activity periods. Our approach is probabilistic and extends recent results of Boxma (1996a,b) who considered the special case of
regular variation.
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