  We consider the stability of robust scheduling policies for multiclass
queueing networks. These are open networks with arbitrary routing matrix and
several disjoint groups of queues in which at most one queue can be served at a
time. The arrival and potential service processes and routing decisions at the
queues are independent, stationary and ergodic. A scheduling policy is called
robust if it does not depend on the arrival and service rates nor on the
routing probabilities. A policy is called throughput-optimal if it makes the
system stable whenever the parameters are such that the system can be stable.
We propose two robust polices: longest-queue scheduling and a new policy called
longest-dominating-queue scheduling. We show that longest-queue scheduling is
throughput-optimal for two groups of two queues. We also prove the
throughput-optimality of longest-dominating-queue scheduling when the network
topology is acyclic, for an arbitrary number of groups and queues.
