Computer Networks

1:

Given an infinite amount of buffer space. In the text it was stated that a satellite with two uplink and one downlink slotted ALOHA channels can achieve a downlink utilization of

A.

0.536

B.

0.636

C.

0.736

D.

0.936

 

Answer : C

Explanation :

The probability of success (i.e. exactly one frame in a slot) = 1 / e  ~ 0.368.
Then probability of a failure (no frames or multiple frames) = 0.632.
Thus joint probabilities of the two uplink channels are :
success on 1 and success on 2 : 0.135 (2 frames sent)
success on 1 and failure on 2 : 0.233 (1 frame sent)
failure on 1 and success on 2 : 0.233 (1 frame sent)
failure on 1 and success on 2 : 0.399 (0 frames sent)
Then expected number of success per slot.
E = 0.35 * x + 0.233 * 1 + 0.233 * 1 + 0.399 * 0 = 0.270 + 0.233 + 0.233 = 0.736 

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Option: A

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