P11. Suppose four active nodes-nodes A, B, C and D–are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability p. The first slot is numbered slot 1, the second slot is numbered slot 2, and so on. a. What is the probability that node A succeeds for the first time in slot 5? b. What is the probability that some node (either A, B, C or D) succeeds in slot 4? c. What is the probability that the first success occurs in slot 3? d. What is the efficiency of this four-node system?

Computer Networking: A Top-Down Approach (7th Edition)
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P11. Suppose four active nodes-nodes A, B, C and D-are competing for
access to a channel using slotted ALOHA. Assume each node has an infinite
number of packets to send. Each node attempts to transmit in each slot with
probability p. The first slot is numbered slot 1, the second slot is numbered slot 2,
and so on.
a. What is the probability that node A succeeds for the first time in slot 5?
b. What is the probability that some node (either A, B, C or D) succeeds in slot
4?
c. What is the probability that the first success occurs in slot 3?
d. What is the efficiency of this four-node system?
Transcribed Image Text:P11. Suppose four active nodes-nodes A, B, C and D-are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability p. The first slot is numbered slot 1, the second slot is numbered slot 2, and so on. a. What is the probability that node A succeeds for the first time in slot 5? b. What is the probability that some node (either A, B, C or D) succeeds in slot 4? c. What is the probability that the first success occurs in slot 3? d. What is the efficiency of this four-node system?
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