A Note on Bounds in the SMP Fluid Models

Authors:
Zbigniew Palmowski
Affiliations:
Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

In this paper we consider a SMP fluid model when the so-called BSNE has no solution and kernel distributions of input environment processes are not heavy-tailed. We prove that in this case we still can find the upper exponential bound for the buffer overflow probability and give the example showing that the lower bound is impossible in general.