Problem 4 Consider the problem faced by a ctitious news service Dhd, who maintains a web page where users may view news items on demand. Response-time is critical in determining the protability of the DW web service: utilization is inversely proportional to perceived latency and advertisers are attracted to news services that are heavily utilized. To minimize perceived latency, DMM has decided to \"mirror\" its website at several locations around the Internet in an e'ort to bring its content closer to users in various part of the world. In this problem, we will consider some of the tradeoffs involved in making this distributedcontent scheme work. The Internet is actually a network of networks, all interacting with a common set of networking protocols, e.g. TUP If IP. There is a natural hierarchy in the Internet whereby individual users, households, and even small Internet service providers buy Internet service from larger Internet service providers, who in turn buy service from even larger providers. At the top, there are thirty or so \"backbone" networks, known as \"peer providers," who are connected to one another at very high data rates and collectively provide Internet connectivity around the world. Let N denote the number of peer providers, and let us refer to them simply as '61, i2,. . Wm. Each backbone network is comprised of a large and very distributed network of individual \"routers which send Internet traic [packets] from point to point. Typically, the paths that packets follow in the Internet are xed in \"routing tables\" and change only when there are outages and link failures. Thus, a common notion of distance between any two points in the Internet is the number of router hops that packets experience in going 'om one backbone ISP to another. Let nli-ij, it} denote the number of router hops that separate backbone networks 'ij and Elk. Service providers often assume, for planning purposes, that the delay experienced by packets traveling om i,- to it, or viceversa, is proportional to HIE-ii, 2],]