Section 7.8. Exercises

7.8. Exercises

1.	Consider a packet-switching network for server communications with n nodes. For each of the following topologies, sketch the network, and give the average number of hops between a pair of servers (include the server-to-node link as a hop): Star: one central node with all servers attached to the central node Bidirectional ring: each node connects to two other nodes to form a loop, with each node connected to one server Fully connected: each node is directly connected to all other nodes, with each node connected to one server A ring with n - 1 nodes connected to a central node , with each node in the ring connected to one server.
2.	Figure 7.18 shows a network. Find the least-cost path between the two servers, using Dijkstra's algorithm. Show an iteration graph as the least-cost path is developed. Figure 7.18. Exercises 24 network example
3.	For the network shown in Figure 7.18: Find the least-cost path between the two servers, using the Bellman-Ford algorithm. Show an iteration graph as the least-cost path is developed.
4.	Consider again the network in Figure 7.18. Assume that each link is bidirectional and that the cost of either direction is identical. Find the least-cost path between the two servers, using Dijkstra's algorithm. Show an iteration graph as the least-cost path is developed.
5.	The network shown in Figure 7.19 is a snapshot of a practical consisting of seven routers. The load on each link is normalized to a number indicated on that link. Find the least-cost path between the two routers R1 and R7, using Dijkstra's Algorithm. Show an iteration graph as the least-cost path is developed. Figure 7.19. Exercises 56 network example
6.	For the network shown in Figure 7.19: Find the least-cost path between the two servers, using the Bellman-Ford algorithm. Show an iteration graph as the least-cost path is developed.
7.	The practical network shown in Figure 7.20 is a WAN consisting of seven routers R 1 through R 7 interconnecting four LANs. The load on each link is normalized to a number indicated on that link. Assume that all links are bidirectional with equal indicated load. Find the least-cost path between the two routers R1 and R 7 connecting users A and B, using Dijkstra's algorithm. Show an iteration graph as the least-cost path is developed. Figure 7.20. Exercise 7 network example
8.	The practical network shown in Figure 7.20 is a WAN consisting of seven routers R 1 through R 7 interconnecting four LANs. The load on each link is normalized to a number indicated on that link. Assume that all links are bidirectional with equal indicated load. Find the least-cost path between the two routers R1 and R 7 connecting users A and B, using Bellman-Ford's algorithm. Show an iteration graph as the least-cost path is developed.
9.	The network in Figure 7.21 has six interconnected nodes, A through F. The corresponding blocking probabilities of links are indicated on the corresponding links. For this network, find the overall blocking probability from A to F. Figure 7.21. Exercise 8 network of links
10.	Figure 7.22 shows a large communication network of six interconnected nodes, A through F. The corresponding blocking probabilities of links are indicated on the corresponding links. For this network, find the overall blocking probability from AtoF. Figure 7.22. Exercise 9 network of links
11.	Computer simulation project . Write a computer program to simulate Dijkstra's algorithm for the seven-node network shown in Figure 7.20. Your program must Use a scheme that runs for any hypothetical link cost. Users A and B use the Bellman-Ford algorithm. Compute the least-cost path between any two routers.
12.	Computer simulation project . Write a computer program to simulate the Bellman-Ford algorithm for the seven-node network shown in Figure 7.20. Your program must Use a scheme that runs for any hypothetical link cost. Users A and B use the Bellman-Ford Algorithm. Compute the least-cost path between any two routers.