CS 4873 Computer Networks, Fall 1999 Assignment 5

Due Thursday, December 2 at the start of class
Print out the postscript file: /usr/local/courses/cs4873/fall1999/cover5.ps and use it as your cover sheet. Make sure you show how you got your answer to each problem.

  1. Three identical stations share a slotted Aloha channel.
    1. Write down an equation giving the relationship between S and G.
    2. What is the probability that a given slot will have no transmissions?
    3. What is the probability that a given slot will have a successful transmission?
    4. What is the probability that a given slot will have a collision?

  2. A CSMA/CD system has k stations contending after a collision. Each station chooses one of the next n slots to attempt another transmission.
    1. Find an expression for the probability that there will be a successful transmission in the first slot.
    2. For fixed k, show that the value of n that maximizes the probability in a) is k.

  3. A CSMA/CD uses a binary exponenital backoff with a slot time of 50 microseconds. Suppose that after a long period of inactivity, 256 stations attempt to transmit at the same time and collide. Assuming that there are collisions on all early rounds, how much time does it take before the round with 256 slots is complete? Answer in seconds. Note: The first round completes in 100 microseconds and the second round completes 200 microseconds later so the second round is done after 300 microseconds.

  4. A CSMA/CD uses a linear backoff with a slot time of 50 microseconds. In a linear backoff system, the number of slots on each successive round increases by 1. Suppose that after a long period of inactivity, 256 stations attempt to transmit at the same time and collide. Assuming that there are collisions on all early rounds, how much time does it take before the round with 256 slots is complete? Answer in seconds. Note: The first round completes in 100 microseconds and the second round completes 150 microseconds later so the second round is done after 250 microseconds.

  5. A CSMA/CD system has a 100 meter cable, a fixed frame size of 1000 bits, runs at 10 Mbps, and has a propagation speed of 200 meters per microsecond.
    1. How does the propagation speed compare to that of the speed of light?
    2. How long is a contention slot?
    3. How long does it take to send a frame?
    4. All other things being as described above, what cable lengths would have the contention slot smaller than the frame time?
    5. All other things being as described above, what frame sizes would have the contention slot smaller than the frame time?

  6. At a transmission rate of 10 Mbps and a propagation delay of 200 meters/microsecond, how many meters of cable is the 1-bit delay in a token ring interface equivalent?

  7. A 10 Mbps token ring with 24 stations is designed to allow for a maximum frame size of 1000 bits. Each station that has something to send can send at most one frame before giving up the token. What is the maximum delay between the time of generation of a new frame by a station and the start of transmission of a frame by that station?