Question

Suppose that the clock-driven scheme for generating initial sequence numbers is used with a 15-bit wide clock counter. The clock ticks once every 100 msec, and the maximum packet lifetime is \(60 \mathrm{sec}\). How often need resynchronization take place (a) in the worst case? (b) when the data consumes 240 sequence numbers/min?

Short answer

(a) 54.613 minutes; (b) 136.533 minutes.

Step-by-step solution

Determine the range of sequence numbers

The sequence numbers are generated using a 15-bit wide counter. This means the range of sequence numbers is from 0 to \(2^{15} - 1\). Hence, there are \(2^{15}=32768\) distinct sequence numbers possible.

Calculate the wrap-around cycle time

Since the clock counter ticks once every 100 milliseconds, the total time before the sequence numbers wrap around is given by \(32768 \times 100 \text{ ms} = 3276.8 \text{ seconds}.\) So, the counter will take about 54.613 minutes to cycle through all sequence numbers.

Determine the worst case scenario

In the worst case, resynchronization is needed when the sequence numbers wrap around a single cycle, which occurs every 54.613 minutes. This is independent of the maximum packet lifetime of 60 seconds.

Calculate time between resynchronizations for specific data consumption

Given that 240 sequence numbers are consumed per minute, we find how long it takes to consume all sequence numbers by \(\frac{32768}{240} = 136.533\) minutes. Resynchronization will thus be needed every 136.533 minutes in this scenario.

Key concepts

Clock Counter

In the context of sequence numbers, a clock counter plays a vital role in synchronizing data flow. A clock counter with a 15-bit width means it can represent sequence numbers ranging from 0 to \(2^{15} - 1\). This equals 32,768 unique sequence numbers available in total.

Every time the clock ticks, it advances this counter by one. In this exercise, the clock ticks once every 100 milliseconds. Therefore, the clock continuously cycles through these sequence numbers until it reaches the maximum, causing a wrap-around to zero. This cycling is crucial because it determines how efficiently data can be synchronized and limits the need for resynchronization.

Packet Lifetime

Understanding packet lifetime is essential to ensure data remains valid during its transit. In this context, the packet lifetime is the duration for which a sequence number, once used, needs to remain unique and cannot be reused.

The problem states that the maximum packet lifetime is 60 seconds. Therefore, any packet or sequence number cannot be reused until that time has elapsed, ensuring that all transmitted data can be clearly distinguished and organized.

Ensuring a sufficiently large range of sequence numbers within the lifetime of packet ensures avoidance of ambiguity in communication. With packets potentially needing up to 60 seconds before being reused, the display of sequence numbers will recycle or loop after precisely defined intervals to still maintain efficient transmission.

Resynchronization

Resynchronization is a necessary process in computer networks to keep data flow consistent and prevent overlap of sequence numbers, which can lead to errors in data transmission.

If we look at our earlier example, resynchronization will need to happen every 54.613 minutes in a worst-case scenario where the sequence numbers are used solely based on how fast the clock counter cycles.

However, when considering data consumption, if a network consumes 240 sequence numbers every minute, resynchronization becomes necessary every 136.533 minutes. Resynchronization ensures that the counter starts fresh to prevent data corruption or mix-up due to overlaps or rapid consumption.

Wrap-Around Cycle

A wrap-around cycle occurs when the clock counter reaches its maximum count and resets to zero. This cycle is crucial as it determines when resynchronization must occur. Given that the counter's maximum is 32,768, and ticks happen every 100 milliseconds, the counter will take 3,276.8 seconds, or about 54.613 minutes, to complete a full cycle.

It is essential to manage this wrap-around to avoid overlaps or collisions in sequence numbers, especially given the 60-second packet lifetime. Therefore, understanding the wrap-around cycle informs resynchronization timing to maintain a seamless and error-free communication.

• In the worst-case scenario, resynchronization is needed every wrap-around cycle.
• For high traffic situations, resynchronization might depend on data consumption rates, extending the time between resyncs when the entire sequence range is consumed slower than the counter cycles.