Consider the packet-switching network below with the costs associated with each link indicated. Using Dijkstra's algorithm, find the cost and the next hop of the least-cost path from source node 1 to all other nodes in the network. 2 3 1 .01 .03 .01 3 2 M .01 The number shown next to each link in the network below is the probability of the link failing during the lifetime of a virtual circuit from node 1 to node 7. It is assumed that links fail independently of each other. .05 .02 5 .04 3 .01 2 t 5 2 .01 6 .03 .02 3 .06 5 8 .03 7 (a) Determine a suitable cost metric in order that a shortest path algorithm can be used to determine the most reliable path from 1 to 7 (i.e., the path with largest probability that all links will remain working). (HINT: A shortest path algorithm minimizes a total distance which is derived by adding the length of each link. Hence, you must derive a metric for cost which is additive. You may find the fact that In xxx-1 for values of x close to 1 useful.) (b) Find the probability of remaining intact for the most reliable path and determine the next hop from node 1 in the path. Consider the packet-switching network below with the costs associated with each link indicated. Using Dijkstra's algorithm, find the cost and the next hop of the least-cost path from source node 1 to all other nodes in the network. 2 3 1 .01 .03 .01 3 2 M .01 The number shown next to each link in the network below is the probability of the link failing during the lifetime of a virtual circuit from node 1 to node 7. It is assumed that links fail independently of each other. .05 .02 5 .04 3 .01 2 t 5 2 .01 6 .03 .02 3 .06 5 8 .03 7 (a) Determine a suitable cost metric in order that a shortest path algorithm can be used to determine the most reliable path from 1 to 7 (i.e., the path with largest probability that all links will remain working). (HINT: A shortest path algorithm minimizes a total distance which is derived by adding the length of each link. Hence, you must derive a metric for cost which is additive. You may find the fact that In xxx -1 for values of x close to 1 useful.) (b) Find the probability of remaining intact for the most reliable path and determine the next hop from node 1 in the path.