Let the size of congestion window of a TCP connection be 32 KB when a timeout occurs. The round trip time of the connection is 100 msec and the maximum segment size used is 2 KB. The time taken (in msec) by the TCP connection to get back to 32 KB congestion window is _________.

Given:

• Initial Congestion Window ($ext{cwnd}$) before timeout = $32\text{ KB} = 16\text{ MSS}$ (since $\text{MSS} = 2\text{ KB}$)

• $\text{RTT} = 100\text{ msec}$

When a timeout occurs in TCP Tahoe/Reno:

• The slow-start threshold is set to $\text{ssthresh} = \frac{\text{cwnd}}{2} = \frac{32\text{ KB}}{2} = 16\text{ KB} = 8\text{ MSS}$.

• $\text{cwnd}$ resets to $1\text{ MSS} = 2\text{ KB}$.

Phase 1: Slow Start (exponential growth until $\text{cwnd} = \text{ssthresh}$):

• At start ($t = 0\text{ RTT}$): $\text{cwnd} = 1\text{ MSS} = 2\text{ KB}$

• After $1\text{ RTT}$: $\text{cwnd} = 2\text{ MSS} = 4\text{ KB}$

• After $2\text{ RTT}$: $\text{cwnd} = 4\text{ MSS} = 8\text{ KB}$

• After $3\text{ RTT}$: $\text{cwnd} = 8\text{ MSS} = 16\text{ KB}$ (reaches $\text{ssthresh}$)

Phase 2: Congestion Avoidance (linear growth by $1\text{ MSS}$ per RTT):

• After $4\text{ RTT}$: $\text{cwnd} = 9\text{ MSS} = 18\text{ KB}$

• After $5\text{ RTT}$: $\text{cwnd} = 10\text{ MSS} = 20\text{ KB}$

• After $6\text{ RTT}$: $\text{cwnd} = 11\text{ MSS} = 22\text{ KB}$

• After $7\text{ RTT}$: $\text{cwnd} = 12\text{ MSS} = 24\text{ KB}$

• After $8\text{ RTT}$: $\text{cwnd} = 13\text{ MSS} = 26\text{ KB}$

• After $9\text{ RTT}$: $\text{cwnd} = 14\text{ MSS} = 28\text{ KB}$

• After $10\text{ RTT}$: $\text{cwnd} = 15\text{ MSS} = 30\text{ KB}$

• After $11\text{ RTT}$: $\text{cwnd} = 16\text{ MSS} = 32\text{ KB}$

Total time taken = $11 \times \text{RTT} = 11 \times 100\text{ msec} = 1100\text{ msec}$.

(Depending on whether slow-start transition or timeout detection is counted, the official answer range is 1100 to 1300 msec).