Stability conditions for multiclass uid queueing networksDimitris

We introduce a new method to investigate stability of work-conserving policies in multiclass queueing networks. The method decomposes feasible trajectories and uses linear programming to test stability. We show that this linear program is a necessary and suucient condition for the stability of all work-conserving policies for multiclass uid queueing networks with two stations. Furthermore, we nd new suucient conditions for the stability of multiclass queueing networks involving any number of stations and conjecture that these conditions are also necessary. Previous research had identiied suucient conditions through the use of a particular class (monotone piecewise linear convex) Lyapunov functions. Using linear programming duality, we show that for two-station systems the Lyapunov function approach is equivalent to ours and therefore characterizes stability exactly.