CS 4873 Computer Networks, Fall 1997 Assignment 5

1. Two CSMA/CD stations are each trying to transmit long multiframe files. After each frame is sent they contend for the channel using binary exponential backoff (without a cutoff).
   1. Write down an expression for the probability, Pc_k, that the contention ends on round k given that it has gotten to round k.
   2. Write down an expression which would allow you to caclulate the probability, P_k, that the contention ends on round k. Note that the sum of these should add up to 1.
   3. Write down an expression for the mean number of rounds in a contention period in terms of your answer to b).

2. This problem is a continuation of problem 1.
   1. Write down numerical values for your answer to part 1a) for values of k between 1 and 10. Three places after the decimal point is sufficient. You may need to write a program to do this.
   2. Write down numerical values for your answer to part 1b) forw values if k between 1 and 10. Three places after the decimal point is sufficient. You may need to write a program to do this.
   3. Write down the numerical value of your answer to part 1c) Again, you may have to write a program for this.
   4. Show your calculations for your answers to parts a), b) and c) or turn in the source code for the programs you used to calculate the answers.

3. Sketch the Manchester encoding for the bit stream: 01010011.

4. 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?

5. A 10 Mbps token ring with 24 stations is designed to allow for a maximum frame size of 1000 bits. What is the smallest possible value for 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?