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Suppose TCP uses congestion control without slow start.The first transmission start with 1 MSS,  Assuming cwnd increases by 3 MSS every time a batch of ACKs is received and assuming approximately constant round-­?trip times, the next window after timeout will be the the size of new threshold,  if timeout occurs at the sixth transmission, how many total round trip time requires to reach the window size of 20 MSS.

First transmission = 1 MSS

Second transmission= 4 MSS

Third transmission = 7 MSS

Fourth transmission= 10 MSS

Fifth transmission= 13 MSS

Sixth transmission= 16 MSS [ Timeout, New th = 16 / 2 = 8 MSS]

Seventh transmission = 8 MSS

Eight transmission= 11 MSS

Ninth transmission= 14 MSS

Tenth transmission= 17 MSS

At the end of the tenth transmission, the window size reaches 10 MSS

So 10 RTTs are required.

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You took wrong threshold value. In the question it is given that

the next window after timeout will be the the size of new threshold

Hence the new threshold will be next window after 16 i.e 19.

hence that gives the total RTT to be 13