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 so urces. We do not suppose that the model is symmetrical: there is an ar bitrary number K of different traffic classes, and for each class k, a n arbitrary number N-k Of sources of this class. We derive lower and u pper bounds for the stationary distribution of the backlog X of the fo rm B exp(-thetax) less than or equal to P(X > x) less than or equal t o C(theta) exp(-theta x), with 0 less than or equal to theta less than or equal to theta. When K = 2 or K = 1, we numerically compare our b ounds to the exact distribution of X and to other previously known res ults. Through various examples, we discuss the behavior of P(X > x) an d the tightness of the bounds.