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Suppose three active nodes - Nodes A, B and C - 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 1, the second slot is numbered 2, and so on. What is the probability that node A succeeds for the first time in slot 5?

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Answer #1

Suppose 3 active nodes - nodes A, B and C are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send.

Solution :- (1 - P(A)) P(A) where P(A) is the probabilty that A succeeds in a slot.

P(A) = P(A transmits and B does not transmits and c does not transmits and D does not transmits)

= P(A transmits) P(B does not transmits) P(C does not transmits) P(D doe not transmits)

= P(1 -P)(1 - P)(1 - P) = P(1 - P)3

Hence, P(A succeeds first time in slot 2)

Hence, P(A succeeds first time in slot 2)

3 active noden , -№cLeA AIB ard c are (ow/eting accen t a channel sin Slotted ALDHA dtstume cach node hau an nite nunber acket to send. So pia) (A and B deernot trarumith dosrot P(A traunih) PlR dou not tr ururnit) pic does not transmit) Hence PIA Jucce edajnt tirne踟stot 2)

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