GATE CS 2023 Q40 — Transport Layer: Flow Control, Congestion Control, UDP, TCP, Sockets

To prevent sequence number wrap-around within the Maximum Segment Lifetime ($\text{MSL}$), the total number of unique sequence numbers available must be greater than or equal to the maximum number of bytes that can be transmitted during one $\text{MSL}$.

Step 1: Calculate the maximum bytes transmitted in one $\text{MSL}$

• Bandwidth: $100 \text{ Mbps} = 100 \times 10^6 \text{ bits/second}$
• Bandwidth in Bytes: $$\text{Bandwidth} = \frac{100 \times 10^6}{8} \text{ bytes/second} = 12.5 \times 10^6 \text{ bytes/second}$$
• Maximum Segment Lifetime (MSL): $2 \text{ minutes} = 120 \text{ seconds}$
• Total bytes transmitted in MSL: $$\text{Total Bytes} = 12.5 \times 10^6 \text{ bytes/second} \times 120 \text{ seconds} = 1.5 \times 10^9 \text{ bytes}$$

Step 2: Determine the minimum sequence number field length ($N$)

For a sequence number field of $N$ bits, the sequence number space is $2^N$. To avoid wrap-around within the MSL, we require:

Let's evaluate the powers of $2$:

• For $N = 30$ bits: $2^{30} \approx 1.07 \times 10^9 < 1.5 \times 10^9$ (Insufficient)
• For $N = 31$ bits: $2^{31} \approx 2.15 \times 10^9 \ge 1.5 \times 10^9$ (Sufficient)

Thus, the minimum length of the sequence number field must be at least $31$ bits. Any length $N \ge 31$ is valid.

Conclusion

• A. $30$ bits: Invalid ($30 < 31$)
• B. $32$ bits: Valid ($32 \ge 31$)
• C. $34$ bits: Valid ($34 \ge 31$)
• D. $36$ bits: Valid ($36 \ge 31$)