1 EE555, Broadband Network Architecture HW7, Due Dec 11 (in my office) Problems Assignment #6 1. What is the size of the multicast address space? What is the probability that two different multicast groups choose the same the same multicast address? 2. Suppose that a network consists of "G" multicast groups, each with "S" group members, each of which can be a sender. Under DVMRP, each router must maintain up to "S" pieces of routing information (The outgoing link on the shortest reverse path back to the sender, i.e. the parent port, for each of the "S" senders) for each group. Thus, in the worst-case scenario, 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-DM and PIM-SP? Justify your answers. 3. The multicast host model does not define any interaction between the multicast sources and IGMP (i.e. the multicast source does not know where (if any) group members are located. Do you see any problems with that? Explain. Hint: Think of a case where there are no members for a group. A researcher suggested that the "multicast source" multicast a query to the group in order to find out whether there are members in the group or not. Receivers would respond to this query by sending response to the source. Based on your answer to the first part of this question, do you think that helps to solve the problem and how? What is a main problem associated with this approach (the multicast query/response)? Suggest two alternative modifications to alleviate this problem. {Hint: You may use timers at the receivers, but how? You may also suggest simple modifications to IGMP}24. Consider the network shown below. Suppose a multicast source is connected to R7 wishes to send Packets to multicast group designated by G1 (shaded in diagram). Find the set of paths that are obtained from Reverse Path Multicasting, RPM (clearly state your assumptions as far as the parent/child ports are concerned along with pruning messages, if any) 5. Stalling's Book, Chapter 16, Problems: 2, 3 6. Consider an optical network with 8 nodes. Each node can transmit and receive on two wavelengths. Each wavelength can support X bps. Traffic is uniform. You are to consider various designs and find the maximum throughput. All nodes share a single medium (passive star) but different logical topologies are used  The nodes are connected in a bi-directional ring fashion (i.e. node x is connected to the node x-1 and to node x+1, mod 8 of course)  8-node perfect shuffle For each of these networks: a) Sketch the network connections between nodes b) Sketch the path from node 1 to all other nodes (Note: Do not consider the case when a node sends to itself) c) Compute: 1. The average number of hops 2. The total (aggregate) capacity R1 R2 R3 R5R4R7R8R633. The capacity per user (in terms of X). Which network provides the maximum capacity/user? d) Draw the physical bus topology with wavelength (λ) assignments, for the 8-node bi-directional ring logical topology above. How many wavelengths are needed. Suggest another physical topology that may reduce this number by 1/2 e) For the bi-directional ring topology, suppose node 8 fails. Sketch the path from node 1 to all other nodes and find the average number of hops, the traffic that is generated at node 1 and destined to nodes 2 through 7, will encounter. Assume uniform traffic. How would you rearrange the wavelength assignments to minimize the average number of hops for node