Consider an instance of TCP's Additive Increase Multiplicative Decrease (AIMD) algorithm where the window size at the start of the slow start phase is 2 MSS and the threshold at the start of the first transmission is 8 MSS. Assume that a timeout occurs during the fifth transmission. Find the congestion window size at the end of the tenth transmission.

Let us trace the congestion window ($cwnd$) and slow-start threshold ($ssthresh$):

• Initial Conditions:

  • Starting $cwnd = 2\text{ MSS}$

  • Initial $ssthresh = 8\text{ MSS}$

• Transmission Schedule:

  • Transmission 1: $cwnd = 2\text{ MSS}$ (Slow Start). Successful $\implies cwnd$ doubles to $4\text{ MSS}$.

  • Transmission 2: $cwnd = 4\text{ MSS}$ (Slow Start). Successful $\implies cwnd$ doubles to $8\text{ MSS}$ (reaches $ssthresh$).

  • Transmission 3: $cwnd = 8\text{ MSS}$ (Congestion Avoidance). Successful $\implies cwnd$ increases by $1$ to $9\text{ MSS}$.

  • Transmission 4: $cwnd = 9\text{ MSS}$ (Congestion Avoidance). Successful $\implies cwnd$ increases by $1$ to $10\text{ MSS}$.

  • Transmission 5: $cwnd = 10\text{ MSS}$. A timeout occurs.

• Reaction to Timeout:

  • $ssthresh = \max\left(2, \left\lfloor\frac{cwnd}{2}\right\rfloor\right) = \frac{10}{2} = 5\text{ MSS}$.

  • $cwnd$ resets to the slow-start window (typically $1\text{ MSS}$, or $2\text{ MSS}$ as stated at the start of the slow-start phase).

• Subsequent Transmissions (assuming reset to $2\text{ MSS}$):

  • Transmission 6: $cwnd = 2\text{ MSS}$ (Slow Start) $\implies cwnd$ becomes $4\text{ MSS}$.

  • Transmission 7: $cwnd = 4\text{ MSS}$ (Slow Start) $\implies cwnd$ reaches threshold $5\text{ MSS}$.

  • Transmission 8: $cwnd = 5\text{ MSS}$ (Congestion Avoidance) $\implies cwnd$ becomes $6\text{ MSS}$.

  • Transmission 9: $cwnd = 6\text{ MSS}$ (Congestion Avoidance) $\implies cwnd$ becomes $7\text{ MSS}$.

  • Transmission 10: $cwnd = 7\text{ MSS}$ (Congestion Avoidance) $\implies cwnd$ at the end of 10th transmission becomes $8\text{ MSS}$.

Due to ambiguities in whether $cwnd$ resets to $1\text{ MSS}$ (RFC standard) or $2\text{ MSS}$, and the interpretation of window size "during" vs "at the end of" the tenth transmission, this question was awarded Marks to All in the official answer key.