Question 50

To prevent old duplicate packets from causing confusion, sequence numbers must not wrap around within the Maximum Segment Lifetime (MSL = 2 minutes = 120 seconds).

1. Network transmission bandwidth: $R = 100\text{ Mbps} = 100 \times 10^6\text{ bits/s} = 12.5 \times 10^6\text{ bytes/s}$.
2. Maximum bytes transmitted in $\text{MSL} = 120\text{ seconds}$:
   $$\text{Bytes} = 12.5 \times 10^6 \times 120 = 1.5 \times 10^9\text{ bytes}$$
3. Minimum number of bits $k$ required to provide unique sequence numbers:
   $$2^k > 1.5 \times 10^9$$
   • $2^{30} \approx 1.074 \times 10^9 < 1.5 \times 10^9$ (Insufficient)
   • $2^{31} \approx 2.147 \times 10^9 > 1.5 \times 10^9$ (Sufficient)
4. Any header field length $k \ge 31$ bits will prevent wrap-around. Therefore, 32 bits, 34 bits, and 36 bits are all valid lengths.