We study the scheduling policies for high-speed communication networks with time varying traffic patterns. We model such networks as open multiclass queueing networks operating in a slowly changing environment.

We assume that there are finite environment states and the changing environment is modeled as a general stochastic process which takes discrete values. At each state of the environment, the network operates as a queueing network where each server may serve multiple classes of customers. In this study, we establish a framework to search for asymptotically optimal scheduling policies for such queueing networks. We first show that open queueing networks in a slowly changing environment can be approximated by their fluid analog, stochastic fluid models, when the network speed increases. Given a solution of the stochastic fluid model, we provide a method to derive suitable scheduling policies for the original queueing networks. We further show that the queueing networks operating under the derived policies converge to the corresponding stochastic fluid model . This result implies that the derived scheduling policies are asymptotically optimal if the given stochastic fluid model solution is optimal. We also study a stochastic fluid model to investigate the optimal resource allocation policies of Web servers serving heterogeneous classes where the Web servers may be overloaded and operate under Quality of Service contracts.