CS 4873 Computer Networks, Fall 1999 Assignment 4

Due Thursday, November 11 at the start of class
Note that this is a short 1-week assignment.

Print out the postscript file: /usr/local/courses/cs4873/fall1999/cover4.ps and use it as your cover sheet. Make sure you show how you got your answer to each problem.

  1. Consider a pure Aloha system with a large number of stations.
    Assume that 10 percent of transmissions produce collisions.
    1. What is the probability that a transmission will be successful?
    2. What is the channel load, G?
    3. What is the throughput, S?
    4. What is the average number of attempts needed for a successful

  2. A pure Aloha system has 1000 identical stations. Frames are 100 bits each and the data rate of the channel is 4 Mbps. A measurement of the system shows that the probability that a transmitted frame will be transmitted successfully is 0.5.
    1. What is the channel load, G?
    2. What is the throughput, S?
    3. What is the average number of attempts needed for a successful transmission?
    4. How many new frames per second are generated by one of the stations?

  3. A slotted Aloha system has 1000 identical stations. Frames are 100 bits each and the data rate of the channel is 4 Mbps. A measurement of the system shows that 6 percent of the slots are empty.
    1. What is the channel load, G?
    2. What is the throughput, S?
    3. What is the average number of attempts needed for a successful transmission?

  4. A slotted Aloha system has 1000 identical stations. Frames are 100 bits each and the data rate of the channel is 4 Mbps. A measurement of the system shows that 81.24 percent of the slots are empty.
    1. What is the channel load, G?
    2. What is the throughput, S? Compare your answer to 3b.
    3. What is the average number of attempts needed for a successful transmission?

  5. A slotted Aloha system has 1000 identical stations. Frames are 100 bits each and the data rate of the channel is 4 Mbps. Each station generates 5 new frames per second.
    1. What is the channel load, G?
    2. What is the throughput, S?
    3. What is the average number of attempts needed for a successful transmission?
    Hint: Be careful on this one. Explain how you got your answers.

  6. Four identical stations share a slotted Aloha channel. Note that 4 is not a large number.
    1. Write down an equation giving the relationship between S and G.
    2. Show that the maximum value of S occurs when G = 1.
    3. What is the maximum value of S?
    4. Is this maximum value bigger or smaller than in the case of an infinite number of users?

  7. Suppose that the slotted Aloha system in the previous problem is running at maximum efficiency, G = 1.
    What is the probability that a given slot will have:
    1. no transmissions
    2. a successful transmission
    3. a collision

  8. Twenty identical stations share a slotted Aloha channel. Do not assume that 20 is a large number.
    1. Write down an equation giving the relationship between S and G.
    2. The maximum value of S occurs at G=1. What is the maximum value of S?
    3. Is this maximum value bigger or smaller than in the case of 4 users (Problem 6)?

  9. Twenty identical stations share a slotted Aloha channel which is running at maximum efficiency, G = 1. Do not assume that 20 is a large number.
    What is the probability that a given slot will have:
    1. no transmissions
    2. a successful transmission
    3. a collision

  10. Suppose that an infinite slotted Aloha system is running at maximum efficiency, G = 1.
    What is the probability that a given slot will have:
    1. no transmissions
    2. a successful transmission
    3. a collision
    Compare your answers with those of Problem 9.