Problems 1. [50 points] Consider a three-layer protocol in which Layer 3 encapsulates Layer 2 and Layer 2 encapsulates Layer1. Assume minimalist headers with fixed length packets. Assume the following characteristics of the layers: Layer 1, 6 octet address length, 512 octet payload; Layer 2, 4 octet address length, 256 octet payload; Layer 3, 8 octet address length, 1024 octet payload. Note that in the minimalist header arrangement, no error detection or correction will be used; however, there must be a scheme (that you must devise) to allow a multipacket datagram at each separate layer. You may assume that there is some sort of routing or other address translation protocol that will identify which addresses are to be used. Assume that the data communications channel in use do form a data communications network. (Hint: do recall what is needed for a data communications network as contrasted with an arbitrary graph.) 1.1. For each of the three layers, separately calculated, how many items(nodes) can be addressed? Do not simply show an answer, but explain your reasoning (hint: combinatorics) 1.2. Assume that the datagram has 5 layer 1 packets. How does this datagram encapsulate in layer 2?) 1.3. Taking the above result, or a made-up one of your choosing if you cannot calculate such a result, how does this data from 1.4. Assuming that the only information of interest is the payload of layer1, what is the overall efficiency of the final 1.5. Assuming that only the information in the starting layer 1 datagram payload is the signal, and the rest is noise, what is layer 2 encapsulating layer 1 data then encapsulate in layer 3? encapsulated data stream in layer 3 for the layer 1 datagram described above? the effective Shannon-Hartley theorem relation between "channel capacity" and "bandwidth" for this specific datagram? 2. [50 points] Consider a set of intersecting rings as in the following figure. Here, a small square represents a node, including nodes that can transfer packets between rings, and each ring has an arrow that indicates the direction of packet flow on that ring. 2.1. Display the adjacency matrix for the network in the figure. 2.2. Which, if any, nodes are equivalent on the network and why? 2.3. Display the weight matrix for the network. 2.4. Using Dykstra's algorithm, calculate a route from node S to node D on the network as displayed in Fig. 1. Show each step of the algorithm as you develop the route Figure 1: A Network of Intersecting Rings