Abstract: In the late 90’s, Frank Kelly of Cambridge University and other researchers discovered that many of the protocols that control internet traffic congestion and routing can be expressed in terms of algorithms that solve a convex optimization problem. The objective function to be maximized incorporates efficient utilization and fair allocation of network resources among its users. We will discuss a model of TCP congestion control and routing that arises from such an optimization problem and along the way, show how topics in undergraduate mathematics play a role in its analysis.