Given the importance of communication services, such as those provided by telecommunications and the Internet, the problem of designing their networks has been extensively investigated by researchers in Management Science/Operations Research. Particularly, there is much research determining appropriate routing systems. However, given recent improvements in routing technologies and the potential growth in services which require more computing resources, it has become important for service

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... rs to examine their networks from a processing capacity point of view, as these resources are a new potential bottleneck. This thesis presents models that mathematically describe aspects of processing investment and service provision, given distributed processing in modem communication networks. Unlike previous research, aspects considered include delivery times, quality of service, and congestion. The model developed is different from the standard capacity expansion/facility location models in that the capacity decisions implicitly influence demand. The mathematical models developed in this thesis for the capacity investment problem contain integer decision variables and uncertain parameters in a two-stage stochastic integer programming framework. These aspects add significant complexity to the model. Therefore, another important contribution of this thesis is the investigation into the impact of making model approximations to reduce this complexity. This enables better understanding of the model by illustrating the relative importance of the model's complex aspects.