Data Communications II, Autumn 2003

Problem set 4 (15.10.2003)

1. Consider one sender and 32 receivers. Suppose the sender is connected to the receivers through a binary tree of routers. The sender is the root and the receivers are the leaves in the tree and in each node between has a router. The sender sents a packet first to the next router, that sends it to the router below etc until the packet reaches the the receiver.

   1. How many sendings alltogether are needed if a separate packet is sent to each receiver?
   2. How many sendings are needed, if the packet is sent as a multicast packet to each receiver?

2. Suppose node C is chosen as the center in a center-based multicast routing algorithm. Assuming that each attached router in the multicast group (= A, B, E and F) uses its least-cost path to node C, show the resulting center-based multicast routing tree. Is the resulting tree a minimum-cost Steiner tree?

                  1             1
          B ------------ D ------------ E
          | .                          .|
          |  .                       .  |
          |   .                    .    |
          |    . 2             2 .      |
        4 |     .              .        | 1
          |      .           .          |
          |       .        .            |
          |        .     .              |
          |         .  .                |
          A -------- C ---------------  F
               3             2
   

3. Supposing that in the net of the previous problem the cost of the link BC becomes fivefold, that is changes to 10. Find the Steiner tree that connects all the nodes A, B, E and F belonging to the group. It is not necessary to use the Steiner tree construction algorithm. It is enough to inspect the net in order to find the Steiner tree.

4. Consider the network below. Supposing that the link costs are equal on all links, what kind of "reverse path forwarding" -tree would you make for node F? How is this tree actually formed? When node F sends a broadcast packet, how many packets are really sent in the subnetwork?

                B --------------------------------------------- C
                |                                               |
         E -----|---------------------------- A                 |
         |      |                             |                 |
         |      |                             |                 |
         H -----|------------ I ------------- F --------------- D
         |      |             | .                               |
         |      L             |  .                              |
         |     .              |   .                             |
         |    .               |    .                            |
         |   .                |     .                           |
         |  .                 |      .                          |
         | .                  |       .                         |
         |.                   |        .                        |
         K -------- M ------- N -- O -- J --------------------- G
   
    

5. The researcher Eri Etevä from the University of Helsinki is visiting universities and research institutes in USA that are of importance to his field of research. He stays a couple of days in one place and then moves along to another place. He carries with him his personal PC to store all the important and necessary information.
   1. How can he, when staying a few days in the university B as a visiting reseacher, send email using his own PC?
   2. The members of his research group in Helsinki are sending him the results of a test series and want his opinion on a recent problem in tests. How are these messages between Helsinki and university B routed in Internet?
   3. How does the communication and the routing change if Mobile IP is used?
   4. How does GSM network route messages to the mobile phone of Etevä, providing that his phone can also be used in USA?

6. Find out what kind of wireless LAN services are available in Finland (or in some other country). Where are these WLANs available and how can one get to use them? What WLAN technologies are used in these WLANs? What services do they provide? Is the wireless data communication more secure than communication through wires and cables?