Dynamic Scheduling of Open Multiclass Queueing Networks in a Slowly Changing Environment
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This thesis investigates the dynamic scheduling of computer communication networks that can be periodically overloaded. Such networks are modelled as mutliclass queueing networks in a slowly changing environment. A hierarchy framework is established to search for a suitable scheduling policy for such networks through its connection with stochastic fluid models. In this work, the dynamic scheduling of a specific multiclass stochastic fluid model is studied first. Then, a bridge between the scheduling of stochastic fluid models and that of the queueing networks in a changing environment is established. In the multiclass stochastic fluid model, the focus is on a system with two fluid classes and a single server whose capacity can be shared arbitrarily among these two classes. The server may be overloaded transiently and it is under a quality of service contract which is indicated by a threshold value of each class. Whenever the fluid level of a certain class is above the designated threshold value, the penalty cost is incurred to the server. The optimal and asymptotically optimal resource allocation policies are specified for such a stochastic fluid model. Afterwards, a connection between the optimization of the queueing networks and that of the stochastic fluid models is established. This connection involves two steps. The first step is to approximate such networks by their corresponding stochastic fluid models with a proper scaling method. The second step is to construct a suitable policy for the queueing network through a successful interpretation of the stochastic fluid model solution, where the interpretation method is provided in this study. The results developed in this thesis facilitate the process of searching for a nearly optimal scheduling policy for queueing networks in a slowly changing environment.