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hosts that are participating in a multicast group 11) Consider the two basic approaches identified towards achieving multicast: unicast emulation and network-layer-multicast Consider a single sender and 32 receivers Suppose the sender is connected to the receiver through a binary tree of routers What is the cost of sending a multicast packet in the case of unicast emulation and network-layer multicast for this topology Here, each time a packet (or copy of a packet) is sent over a single link, it incurs a unit of "cost" What topology for interconnecting the sender, receivers, and routers will bring the cost of unicast emulation and true network-layer-multicast as far apart as possible You can choose as many routers as you'd like 12) Design (give a pseudocode description of) an application-level protocol that maintains the host addresses of all hosts participating in a multicast group Specifically identify the network service (unicast or multicast) that is used by your protocol, and indicate whether your protocol is sending messages in-band or out-of-band (with respect to the application-data flow among the multicast group participants), and why 13) Consider the topology from Figure 48-8 Suppose the link cost from B to D changes from 1 to 10 Find the Steiner tree that connects all of the shaded routers (Note: you are not being asked here to program a solution to the Steiner tree problem Instead, you should be able to construct the minimum costs tree by inspection and informally convince yourself that it is the minimum costs tree) If you were asked (you are not being asked to actually do so!), how would you prove that your tree is indeed a minimum cost tree 14) Center-based routing Consider the topology shown in Figure 48-8 Suppose node C is chosen as the center in a center-based multicast routing algorithm Assuming that each attached router in the multicast group uses its least cost path to node C to send join messages to C, draw the resulting centerbased multicast routing tree Is the resulting tree a minimum cost Steiner tree Justify your answer 15) Least unicast-cost path routing Consider Figure 48-8 Suppose that node E is chosen as the source Compute the least unicast-cost path multicast routing tree from E to multicast routers A, B, and F 16) Reverse path forwarding Consider the topology and link costs shown in Figure 48-8 and suppose that node E is the multicast source Using arrows like those shown in Figure 48-11, indicate links over which packets will be forwarded using RPF, and links over which packets will not be forwarded, given that node E is the source 17) Suppose that the cost of a transmitting a multicast packet on a link is completely independent of the cost of transmitting a unicast packet on a link Will reverse path forwarding still work in this case Justify your answer 18) Traffic concentration in center-based trees Consider the simple topology shown in Figure 48-8 Suppose that each of the multicast routers receive one unit of traffic per unit time from an attached host
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file:///D|/Downloads/Livros/computa o/Computer%20N20Approach%20Featuring%20the%20Internet/ROUT_HWHTM (6 of 9)20/11/2004 15:52:30
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Homework Problems and Discussion Questions, 4
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This traffic must be forwarded to the other three multicast routers Suppose that node C is chosen as the center node in a center-based multicast routing protocol (see homework problem above) Given the resulting routing tree, compute the rate of traffic on each link in the topology (Compute the total amount of traffic on each link, regardless of the direction of the traffic flow) Suppose next that RPF is used to build four source-specific routing trees rooted at each of the routers A, B, E, F Recompute the rate of traffic on each of the links in this second scenario In this example, does a center-based tree or sourcespecific trees tend to concentrate traffic 19) Suppose that a network has G multicast groups, each with S group members (hosts), each of which can be a sender Under DVMRP, each router must thus maintain up to S pieces of routing information (the outgoing link on the shortest reverse path to the sender, for each of the S senders) for each group Thus, in the worst case, each router must maintain S*G pieces of routing information, when taking all groups into account What is the worst case amount of routing information needed by MOSPF, PIM Sparse Mode and PIM Dense Mode Justify your answers 20) Birthday problem What is the size of the mutlicast address space Suppose now that two different multicast groups randomly choose a multicast address What is the probability that they choose the same address Suppose now that 1000 multicast groups are ongoing at the same time and chose their multicast group addresses at random What is the probability that they interfere with each other 21) Recall that in our discussion of multicast tunneling, we said that an IP multicast datagram is carried inside of a IP unicast datagram How does the IP router at the end of the multicast tunnel know that the unicast datagram contains an IP multicast datagram (as opposed to simply being an IP unicast datagram that should be forwarded along)
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