With the rising popularity of Voice over IP (VoIP) services, understanding the effects of a global network on Quality of Service is critical for the providers of VoIP applications. This thesis builds on a model that analyzes the round trip time, packet delay jitter, and packet loss between endpoints on an Autonomous System (AS) level, extending it by mapping AS pairs onto an Internet topology. This model is used to produce a mean opinion score estimate. The mapping is introduced to reduce the size of the problem in order to improve computation times and improve accuracy of estimates. The results of testing show that estimating mean opinion score from this model is not desirable. It also shows that the path mapping does not affect accuracy, but does improve computation times as the input data grows in volume.