Abstract
We present an intuitive stability condition for open multiclass queueing networks with Bernoulli routing: if each station has enough service capacity to cope with its peak traffic intensity, then the network is stable under any stationary nonidling scheduling policy. The condition is close to sharp for networks with light traffic between stations. Under this peak-rate condition, in the case of Markovian networks, we derive a closed-form upper bound on the time-average number of customers in the system, which is uniformly valid under all stationary nonidling policies. Our proof combines two recent results concerning (1) the relation between stability and performance via linear programming developed by Kumar and Meyn (1996); and (2) the work decomposition laws for multiclass queueing networks of Bertsimas and Ni?o-Mora (1999). The stability condition is tested on a generalization of the Lu-Kumar network, which shows how its quality depends on the degree of network connectivity.
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