Upper and lower bounds for the multiplexing of multiclass Markovian on/off sources

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 Nk of sources of this class. We derive lower and upper bounds for the stationary distribution of the backlog X of the form B exp(−θ∗x) ≤ P(X > x) ≤ C(θ) exp(−θx), with 0 ≤ θ ≤ θ∗. 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.