Question

Suppose TCP operates over a 1-Gbps link. (a) Assuming TCP could utilize the full bandwidth continuously, how long would it take the sequence numbers to wrap around completely? (b) Suppose an added 32-bit timestamp field increments 1000 times during the wraparound time you found above. How long would it take for the timestamp to wrap around?

Short answer

a) 34.36 seconds, b) 147,323.84 seconds

Step-by-step solution

- Calculate the Total Number of Sequence Numbers

TCP sequence numbers are 32-bit numbers. Calculate the total number of unique sequence numbers available by using the formula: \( 2^{32} \).

- Convert the Total Number of Sequence Numbers to Bits

Each sequence number represents a byte, so the total number of sequence numbers corresponds to \( 2^{32} \) bytes. Since there are 8 bits in a byte, convert this to bits: \( 2^{32} \times 8 \).

- Calculate the Time to Wrap Around (Part a)

To determine how long it takes to send \( 2^{32} \) bytes over a 1-Gbps link, use the formula: \( \text{Time} = \frac{\text{Total bits}}{\text{Bandwidth}} = \frac{2^{32} \times 8}{10^9} \) seconds.

- Simplify the Time Calculation

Calculate the simplified value: \( \frac{2^{32} \times 8}{10^9} = \frac{34,359,738,368}{1,000,000,000} = 34.36 \) seconds.

- Calculate Timestamp Wraparound (Part b)

The timestamp field increments 1000 times during the sequence number wraparound time of 34.36 seconds. Thus, the time taken for one increment is \( \frac{34.36}{1000} \) seconds. Calculate the total wraparound time for the timestamp field using 32 bits: \( 2^{32} \times \frac{34.36}{1000} \) seconds.

- Simplify the Timestamp Wraparound Time

Calculate the simplified value: \( 2^{32} \times \frac{34.36}{1000} = 34.36 \times 4,294,967.296 = 147,323.84 \) seconds.

Key concepts

32-bit Sequence Numbers

TCP (Transmission Control Protocol) uses 32-bit sequence numbers for managing data packets. A 32-bit sequence number means that you have a total of \(2^{32}\) unique sequence numbers. This is over 4 billion distinct values. When a TCP connection starts, the sequence number begins at a randomly selected value and increments with each byte of data sent.

Due to the 32-bit limit, eventually the sequence numbers will 'wrap around.' This means the sequence number will go back to zero after reaching the maximum value. This will happen every \(2^{32}\) bytes of data. For a high-speed Gigabit connection (1 Gbps), the time to wrap around can be calculated as follows:

• Convert bytes to bits: \(2^{32}\) bytes \(\times 8\) bits/byte.
• Calculate the wraparound time: \(\frac{2^{32} \times 8}{10^9} = 34.36\) seconds.

So, at a speed of 1 Gbps, the sequence numbers will wrap around approximately every 34.36 seconds.

Timestamp Wraparound

To address sequence number wraparound issues, TCP can use 32-bit timestamps, which help manage data packets more effectively over long connections. Normally, a timestamp field might increment several times during a sequence number cycle.

Given that the timestamp increments 1000 times during a sequence number wraparound, we can calculate this more precisely:

• Time per increment: \(\frac{34.36}{1000} = 0.03436\) seconds.
• Total wraparound time for the timestamp: \(2^{32} \times 0.03436 = 147,323.84\) seconds.

Therefore, with 32-bit timestamps, the wraparound period is significantly longer, making it easier to manage and track data packets over extended periods.

Data Transmission Speed

The speed at which data is transmitted over a network link significantly impacts sequence number wraparound and data management. Here, we consider a 1-Gbps connection:

• High-speed data transmission allows for large amounts of data to be sent rapidly.
• This results in quicker sequence number wraparound, needing efficient tracking mechanisms like timestamps.

The data transmission speed (in Gbps) determines how quickly sequence numbers and potentially timestamps wrap around. For instance, on a 1-Gbps link, \(2^{32}\) bytes translate to 34.36 seconds for a full wraparound. Higher speeds would reduce this time, exacerbating wraparound management challenges. In essence, faster data transmission requires sophisticated methods to ensure seamless data flow and tracking.