Question

Two CSMA/CD stations are each trying to transmit long (multiframe) files. After

each frame is sent, they contend for the channel, using the binary exponential backoff

algorithm. What is the probability that the contention ends on round k, and what is the

mean number of rounds per contention period?

Please type answer, please do not hand write. Thank you

Answer 1

The probability that contention ends on round k,

Using backoff exponential algo
At round one they have single slot and they both try to transmit in that and hence collides
At round two there are 2 slots waiting for 0 and 1
At i th round station can choose to wait in any 2^i-1 slots

Probability of choosing any one slot in ith period is 1/(2^i-1)
probability of both station choosing same slot is (1/2^i-1) * (1/2^i-1) = 1/2^2(i-1)

Total probability of choosing any of the 2^i-1
slot is hence P = 2^i-1 * (1/2^2(i-1)) = 1/2^i-1

this is probability of collision in ith round
for success on kth round we should have k-1 round in collison and kth round on success
that is {product i:1 to k-1 }(1/2^i-1) * (1- 1/2^i-1)