Consider a long-lived TCP session with an end-to-end bandwidth of 1 Gbps ($= 10^9$ bits-per-second). The session starts with a sequence number of 1234. The minimum time (in seconds, rounded to the closest integer) before this sequence number can be used again is _______.

TCP sequence numbers are 32 bits wide and count bytes of data.

1. Total sequence numbers available:

   $$2^{32} \text{ sequence numbers} = 2^{32} \text{ bytes}$$

2. Total data in bits before sequence number wrap-around:

   $$\text{Total bits} = 2^{32} \times 8 = 4{,}294{,}967{,}296 \times 8 = 34{,}359{,}738{,}368 \text{ bits}$$

3. Transmission rate (bandwidth):

   $$\text{Bandwidth} = 10^9 \text{ bits/second}$$

4. Wrap-around time:

   $$T = \frac{2^{32} \times 8}{10^9} = \frac{34{,}359{,}738{,}368}{10^9} \approx 34.3597 \text{ seconds}$$

Rounding to the closest integer gives 34.