# Actives nodes, adapter, ethernet

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1. 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?

2. Recall that with the CSMA/CD protocol, the adapter waits K.512 bit times after a collision, where K is drawn randomly. For K = 100, how long does the adapter wait until returning to Step 2 for a 10Mbps Ethernet? For a 100 Mbps Ethernet?

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1. 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?

Probability that A succeeds for the first time in slot 5

= (1 - p(A))^4 p(A), where p(A) = probability that node A succeeds in a slot

p(A) = p(A transmits and B does not transmit and C does not transmit and D does not transmit)

= p(A ...

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