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.