Link costs are symmetric the same in both directions

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Unformatted text preview: ork? (a) Only u may have incorrect routes to any other node. (b) Only u and u’s neighbors may have incorrect routes to any other node. (c) In some topologies, all nodes may have correct routes. (d) Even if no HELLO or advertisements packets are lost and no link or node failures occur, a routing loop may occur. 5. Alyssa P. Hacker is trying to reverse engineer the trees produced by running Dijkstra’s shortest paths algorithm at the nodes in the network shown in Figure 20-8 on the left. She doesn’t know the link costs, but knows that they are all positive. All 15 SECTION 18.6. SUMMARY #" !" !" %" '" $" &" #" %" $" '" &" Figure 18-8: Topology for problem 5. link costs are symmetric (the same in both directions). She also knows that there is exactly one minimum-cost path between any pair of nodes in this network. She discovers that the routing tree computed by Dijkstra’s algorithm at node A looks like the picture in Figure 20-8 on the right. Note that the exact order in which the nodes get added in Dijkstra’s algorithm is not obvious from this picture. (a) Which of A’s links has the highest cost? If there could be more than one, tell us what they are. (b) Which of A’s links has the lowest cost? If there could be more than one, tell us what they are. Alyssa now inspects node C, and finds that it looks like Figure 18-9. She is sure that the bold (not dashed) links belong to the shortest path tree from node C, but is not sure of the dashed links. !" #" &" $" '" %" Figure 18-9: Picture for problems 5(c) and 5(d). (c) List all the dashed links in Figure 18-9 that are guaranteed to be on the routing tree at node C. CHAPTER 18. NETWORK ROUTING - I 16 WITHOUT ANY FAILURES A S1 w3 w1 w0 D C S2 w0 w2 w4 B Figure 18-10: Fishnet topology for problem 6. (d) List all the dashed links in Figure 18-9 that are guaranteed not to be (i.e., surely not) on the routing tree at node C. 6. *PSet* Ben Bitdiddle is responsible for routing in FishNet, shown in Figure 18-10. He gets to pick the costs for the different links (the w’s shown near the links). All the costs are non-negative. Goal: To ensure that the links connecting C to A and C to B , shown as darker lines, carry equal traffic load. All the traffic is generated by S1 and S2 , in some unknown proportion. The rate (offered load) at which S1 and S2 together generate traffic for destinations A, B , and D are rA , rB , and rD , respectively. Each network link has a bandwidth higher than rA + rB + rD . There are no failures. Protocol: FishNet uses link-state routing; each node runs Dijkstra’s algorithm to pick minimum-cost routes. (a) If rA + rD = rB , then what constraints (equations or inequalities) must the link costs satisfy for the goal to be met? Explain your answer. If it’s impossible to meet the goal, say why. (b) If rA = rB = 0 and rD > 0, what constraints must the link costs satisfy for the goal to be met? Explain your answer. If it’s impossible to meet the goal, say why....
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.

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