# Upper and Lower Bounds on Overflow Probabilities for a Multiplexer with Multiclass Markovian Sources

Abstract : In this paper, we consider a multiplexer with constant output rate and infinite buffer capacity fed by independent Markovian fluid on-off sources. We do not suppose that the model is symmetrical: there is an arbitrary number $K$ of different traffic classes, and for each class $k$, an arbitrary number $N_k$ of sources of this class. We derive lower and upper bounds for the stationary distribution of the backlog $X$ of the form $B\exp(-\theta^\star~x) \leq P{X>x} \leq C\exp(-\theta^\star~x)$. When $K=2$ or $K=1$, we numerically compare our bounds to the exact distribution of $X$ and to other previously known results. Through various examples, we discuss the behavior of $P{X>x}$ and the tightness of the bounds.
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Submitted on : Wednesday, May 24, 2006 - 2:10:31 PM
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### Identifiers

• HAL Id : inria-00073959, version 1

### Citation

Damien Artiges, Philippe Nain. Upper and Lower Bounds on Overflow Probabilities for a Multiplexer with Multiclass Markovian Sources. RR-2734, INRIA. 1995. ⟨inria-00073959⟩

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