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 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 . 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 . The transmission time is 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.