Internet connected PCs

  1. You are given the assignment of setting subnet addresses for 5 buildings of your company.
    The number of Internet connected PCs in each building is given in the following table.
    Assume that the 139.179.192.0/18 address block is given to you for this purpose. Use the
    following table to show the addresses of the five subnets that you created.
    Building # of PCs Subnet address (CIDR format)
    1 3000
    2 2200
    3 2000
    4 1500
    5 1000
  2. Consider a graph G(V,E), where V is the set of nodes and E is the set of edges (links). For
    e∈E , let we represent the weight of link e . Assume that each link weight corresponds to
    the probability that the link is operational and that the probability that a path is operational
    is given by the product of the weights of the links constituting the path. Your task is to
    find the most reliable path between each node pair. Assume that an implementation of the
    Dijkstra’s algorithm that computes the least cost path (path with the smallest sum of
    weights) between any pair of nodes in the graph is available to you as a black box. You
    cannot make any changes in the given code. Describe how you can use the
    implementation of the Dijkstra’s algorithm to compute the most reliable paths in the
    network, i.e., the path with the smallest product of weights between each node pair. Justify
    that your solution correctly computes the paths with the highest probability of operation as
    defined above.
  3. The network below uses the distance-vector routing algorithm. Assume the following:
    ● Links have the same cost in both directions.
    ● Nodes exchange their routing info once every second, in perfect synchrony and with
    negligible transmission delays. Specifically, at every t = i, i = 0, 1, 2, 3,…, each node
    sends and receives routing info instantaneously, and updates its routing table; the
    update is completed by time t=i+0.1.
    ● At time t = 0, the link costs are as shown below and the routing tables have been
    stabilized. At time t = 0.5, the cost of the link (3,4) becomes 7. There are no further
    link cost changes.
    ● Route advertisements are only exchanged periodically, i.e., there are no immediate
    route advertisements after a link cost change. Hence the first route advertisement
    after the link cost change at t = 0.5 sec occurs at t = 1.0 sec. Note: However,
    whenever a link cost change occurs, the two nodes at the endpoints of this link
    immediately make corresponding changes in their distance tables.
    ● Assume that the distance vector algorithm does not use poisoned reverse.
    Give the evolution of the distance tables with respect to destination 6. Specifically, give
    the distance table entries for destination 6 at nodes 1-5, for t = 0.1, 0.5, 1.1, 2.1, …, until
    all distance vectors stabilize. Present your final answer in the table given below where
    is the distance vector element denoting the distance from i to j.
    Time, t via
    via via
    via
    via
    2 4 6 1 3 2 4 1 3 5 4 6
    0.1
    0.5
    1.1
    2.1
    3.1
    4.1
    5.1
    6.1
    7.1
    8.1
    9.1
    10.1
  4. Execute the Dijkstra algorithm at node B for the network shown below by filling in the
    following table. In the table, you need to give both the distance D(v) and the previous node
    p(v).
    Step
    N’
    D(C),
    p(C)
    D(D),
    p(D)
    D(E),
    p(E)
    D(F),
    p(F)
    D(G),
    p(G)
    D(H),
    p(H)
    D(I),
    p(I)
    D(J),
    p(J)
    D(K),
    p(K)
  5. The following is the forwarding table at router R, which uses CIDR.
    Destination Network Next Hop
    139.179.39.0 / 25 A
    139.179.39.128 / 25 B
    139.179.72.0 / 26 C
    196.101.153.64 / 26 D
    139.179.0.0 / 16 E
    196.0.0.0 / 8 F
    Suppose packets with the following destination IP addresses arrive at router R. Determine
    to which next hop each of these packets will be forwarded.
    Destination IP Address Next Hop
    139.179.39.130
    139.179.39.165
    139.179.72.66
    196.101.153.127
    196.101.153.130
  6. Suppose the data sequence 01101100110 is transmitted using the generator sequence
  7. Compute the CRC bits and the transmitted bit sequence. Assume that the highest
    order first four bits are errored during transmission. Determine whether the error can be
    detected by CRC.
  8. Consider an Ethernet LAN using CSMA/CD running at 100 Mbits/sec. The propagation
    speed for the signal over the cable is 2x108 m/sec. The distances between the nodes in this
    Ethernet are given in the following table. Ignoring the jamming signal, compute the
    minimum frame size in Bytes so that the CSMA/CD algorithm will work properly for this
    LAN.
    Distance (m) A B C D
    A - 100 150 400
    B 100 - 250 200
    C 150 250 - 250
    D 400 200 250 -
  9. Consider three nodes A, B and C on a 100 Mbits/sec Ethernet. Suppose these three nodes
    are involved in a collision which is the third collision for A’s frame, fourth collision for
    B’s frame and second collision for C’s frame. After the collision is detected (we assume
    that all nodes detect the collision exactly at the same time), nodes calculate their backoff
    times according to the binary exponential backoff algorithm.
    i) What is the probability that the first transmission after the above collision will be a
    successful retransmission by C?
    ii) What is the probability that the first transmission after the above collision will be a
    collision involving all nodes?
    iii) What is the probability that the first transmission after the above collision will be a
    collision involving only nodes A and B?
  10. Consider two nodes A and B on a shared link, and both nodes need to transmit frames to
    node C, which is also on the same broadcast link. Assume that there are no other nodes on
    the shared link that currently want to transmit packets. Assume that we use the Slotted
    Aloha protocol. Suppose that a collision just occurred at time t, when A and B transmitted
    in the same slot.
    i) In this part, assume that each node retransmits the collided frame with probability p in
    each successive slot after t. Express the probability of having a successful time slot in
    terms of p. Find the optimum value of p, which maximizes the probability of a
    successful slot, and the resulting maximum value for probability of a successful time
    slot.
    ii) Calculate the average number of time slots elapsed after time t until both nodes
    successfully transmit their respective frames.
  11. Consider the switched network given below. Assume that the switch tables at time t are as
    follows:
    Switch Table at A
    MAC Addr. Port #
    X 2
    W 4
    U 4
    Z 3
    Switch Table at B
    MAC Addr. Port #
    X 4
    W 1
    After time t, first X sends a frame with destination MAC address Z. Second, Y sends a frame
    with destination MAC address U. Third, Z sends a frame with destination MAC address T.
    Finally, U sends a frame with destination MAC address Y.
    i) Which node(s) will receive X’s frame?
    ii) Which node(s) will receive Y’s frame?
    iii) Which node(s) will receive Z’s frame?
    iv) Which node(s) will receive U’s frame?
    A
    B

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