TCP AIMD: Congestion Window at the End of the 10th Transmission

Given: $cwnd = 2$ MSS at the start of slow start, $ssthresh = 8$ MSS at the first transmission, a timeout occurs during the 5th transmission.

Rules used:

• Slow start (SS): cwnd doubles each RTT (2 -> 4 -> 8 ...) but stops doubling once it reaches ssthresh.
• Congestion avoidance (CA): cwnd grows additively by 1 MSS per RTT.
• Timeout: $ssthresh = cwnd/2$, then $cwnd$ resets to 1 MSS and slow start restarts.

Step 1: Behaviour up to the timeout

At transmission 3 the window hits $8 = ssthresh$, so from transmission 4 onward congestion avoidance adds 1 MSS per RTT: $8 \to 9 \to 10$.

Step 2: Effect of the timeout in the 5th transmission

$$ssthresh_{new} = \frac{10}{2} = 5\ \text{MSS}, \qquad cwnd = 1\ \text{MSS}$$

Step 3: Behaviour after the timeout

Transmission 8 doubles $4 \to 8$ but is capped at the new threshold, $\min(8, 5) = 5$ MSS; with $cwnd = ssthresh = 5$ the connection switches to congestion avoidance, which adds exactly 1 MSS per RTT: $5 \to 6 \to 7$.

Final answer: the congestion window size at the end of the 10th transmission is 7 MSS.