GATE CS 2026 Set 1 Q34 — Transport Layer: Flow Control, Congestion Control, UDP, TCP, Sockets

In TCP slow-start, the congestion window ($cwnd$) starts at $1$ segment and doubles every round-trip time ($RTT = 1\text{ ms}$) as long as $cwnd < ssthresh = 10000$.

Let $k$ denote the $k$-th RTT, which spans the time interval $[k-1, k]$ milliseconds. The number of segments transmitted in the $k$-th RTT is $2^{k-1}$.

The cumulative number of segments sent by the end of the $k$-th RTT (at $t = k$ ms) is given by the geometric sum:

Let's calculate $S_k$ for $k = 10$ and $k = 11$:

• For $k = 10$ (at $t = 10\text{ ms}$): $S_{10} = 2^{10} - 1 = 1023$ segments.
• For $k = 11$ (at $t = 11\text{ ms}$): $S_{11} = 2^{11} - 1 = 2047$ segments.

Since segment number $2000$ lies between $1024$ and $2047$, it is transmitted during the 11th RTT, which corresponds to the time interval $[10, 11)$ ms. Therefore, the start time $t$ of segment $2000$ satisfies: