# Question: A communication system sends data in the form of packets

A communication system sends data in the form of packets of fixed length. Noise in the communication channel may cause a packet to be received incorrectly. If this happens, then the packet is retransmitted. Let the probability that a packet is received incorrectly be q.
(a) Determine the average number of transmissions that are necessary before a packet is received correctly. Draw a state diagram for this problem.
(b) Let the the transmission time be Tt seconds for a packet. If the packet is received incorrectly, then a message is sent back to the transmitter stating that the message was received incorrectly. Let the time for sending such a message be Ta. Assume that if the packet is received correctly that we do not send an acknowledgment. What is the average time for a successful transmission? Draw a state diagram for this problem.
(c) Now suppose there are three nodes. The packet is to be sent from node 1 to node 2 to node 3 without an error. The probability of the packets being received incorrectly at each node is the same and is q. The transmission time is Tt and the time to acknowledge that a packet is received incorrectly is Ta. Draw a state diagram for this problem. Determine the average time for the packet to reach node 3 correctly.

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