An Optimization Problem of Internet Routing
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As the Internet usage grows, existing network infrastructure must deal with increasing demand. One way to deal with this is to increase network capacity, and another, is to set network parameters appropriately. In this dissertation we contribute to the latter approach by determining the unique network paths data must flow over from its origin to its destination, while accounting for an Active Queue Management method, Random Early Detection (RED). We formulate a mixed integer non-linear program to determine the data paths, referred to as a routing policy. We prove that determining an optimal routing policy that accounts for RED is NP-Hard. Furthermore, in order for the generated routing policies to be real-world implementable, also known as realizable, we must determine weights for all arcs in the network such that solving the all pairs shortest path problem using these weights reproduces the routing policies. We show that determining if our generated routing policies are realizable is NP-Hard. Fortunately, using traffic data from three real-world networks, we are able to find realizable routing policies for these networks that account for RED, using an off-the-shelf solver, and policies found perform better than those used in those networks at the time the data was collected.