CMSC 417 Midterm #1 (Spring 1997) - Solution
  1. (15 points) Define or explain the following terms:
    1. count to infinity problem: A problem with distance vector routing that causes it to react slowly of link failures since only a count of hops rather than the full path is exchanged between routers.
    2. packet: a small unit of communication. It can be variable or fixed size, but there is a fixed maximum size.
    3. virtual circuit vs. packet switched: Virtual circuits involve using a connection establishment message to store traffic connection state in a network. Virtual circuits tend to provide static routing for a single connection and thus ensure in-order delivery of packets.
    4. ISDN: Integrated Services Digital Network. A way to provide 2 64kbps circuit switched channels over a single pair of copper wire.
    5. flooding: a way to send information from a source to a destination by sending the traffic over all links. It its pure form is generally leads to infinite traffic, but it can be useful as a basis of comparison. Also, by adding ways to control the flood it becomes a practical algorithm.
  2. (15 points) Consider using a 4khz channel and 16 discrete levels to send data.
    1. What is the maximum possible transmission rate if the channel is noiseless?

      2 H log2 N = 2 4,000 log2 16 = 32,000

    2. What if the signal to noise ratio is 30dB?

      X dB = 10 log10(S/N) 10 = 30 log10(S/N) S/N = 1,000

      H log2(1 + S/N) = 4,000 log2(1 + 1,000) 4,000 log2(1024) = 40,000

  3. (15 Points) A cellular phone system needs to accommodate many users. Explain how the system uses space, frequency, and time division multiplexing.

    Space Division: many cells permit re-use of the same channels in any two non-adjacent cells.

    Frequency Division: the cellular band is divided into 800 separate channels.

    Time Division: frequencies are only allocated when they are in use. Since most cell phones in a single cell are not in use at any one time, this is a type of time division multiplexing.

  4. (20 Points) List the seven layers of the ISO/OSI reference model and for each layer provide an example of a function commonly performed at that layer.

    Application: mail header format

    Presentation: encryption

    Session: cursor movement

    Transport: byte ordering

    Network: routing, congestion control

    Link: sending frames, link errors

    Physical: representation of 0's,1's

  5. (20 points) Consider routing in a network with 200 routers, and on average every router is connected to 4 other routers. Routing information is exchanged every 100msec. How much network bandwidth is used under link-state and distance vector routing to exchange this information. Assume sequence numbers are used to damp flood packets for link-state. Please explain any assumptions you make about the size of routing table entries.


    For each link, each router sends <neighbor id, link state> (2 bytes should be fine)

    For each route update, each router sends a sequence number (4 bytes is safe)

    Therefore each routing message contains: 4 links x 2 bytes/link + 4 bytes = 12 bytes.

    Each routing message travels over every link (flooding with sequence numbers)

    200 routers x 4 links/router / (2 end-points per link) = 400 links.

    Routing messages are send 1/100msec = 10 messages/second

    So 200 routers x 10 msgs/sec-router x 400 links x 12 bytes/msg = 9.6M bytes/sec

    Distance Vector:

    Each routing table entry contains <dest, hop count (metric), next hop> 3 bytes

    Each host maintains a 200 entry routing table

    At each update, each router sends all of its neighbors its entire table

    So 200 routers x 10 updates/sec-router x 4 link/router x 3 x 200 bytes/link = 4.8 MB/sec

  6. (15 points) In a broadcast channel, link bandwidth is wasted due to multiple hosts trying to send at once and canceling each others communication. A simple model of this problem is that time is divided into discrete slots. If a network has n hosts, and the probability of any single host trying to use a slot is p, what fraction of slots are wasted due to collisions?

    A collision is two or more stations sending a once. Let P(x) denote the probability of x stations sending at once.

    P(>=2) = 1 - P(0) - P(1)

    P(0) = (1-P)n

    P(1) = n p (1-P)n-1

    (>=2) = 1 - (1-P)n - n p (1-P)n-1