Question

Suppose a host has a 1-MB file that is to be sent to another host. The file takes 1 second of CPU time to compress \(50 \%\), or 2 seconds to compress \(60 \%\). (a) Calculate the bandwidth at which each compression option takes the same total compression + transmission time. (b) Explain why latency does not affect your answer.

Short answer

The bandwidth is 0.1 MB/sec. Latency does not affect the comparison as it is constant.

Step-by-step solution

Understand the Problem

We need to calculate the file transfer times for two compression options and find the bandwidth at which these times are equal.

Define Variables

Let the original file size be 1 MB. Define the bandwidth as B MB/sec.

Calculate Time for 50% Compression

For 50% compression, the file size becomes 0.5 MB. The time taken for compression is 1 second. The transmission time is \(\frac{0.5}{B}\). The total time is 1 + \(\frac{0.5}{B}\) seconds.

Calculate Time for 60% Compression

For 60% compression, the file size becomes 0.4 MB. The time taken for compression is 2 seconds. The transmission time is \(\frac{0.4}{B}\). The total time is 2 + \(\frac{0.4}{B}\) seconds.

Set Equations Equal

Set the total times from both methods equal to find B: \[ 1 + \frac{0.5}{B} = 2 + \frac{0.4}{B} \]

Solve for Bandwidth (B)

Rearrange to get: \[ 1 - 2 = \frac{0.4}{B} - \frac{0.5}{B} \] \[ -1 = \frac{-0.1}{B} \] \[ B = 0.1 \text{ MB/sec} \]

Explain Why Latency Doesn't Affect the Answer

Latency is a constant delay that does not change with compression. Therefore, it cancels out when comparing total times.

Key concepts

File Transfer

File transfer refers to the process of moving digital files from one computer to another across a network. Whether you are sending an email with attachments, uploading documents to a cloud service, or transferring data between servers, the efficiency of file transfer is paramount.
The performance of file transfer is influenced by factors such as file size, compression methods, and network bandwidth. By compressing files before sending, we can significantly reduce the transfer time.
In the provided exercise, we have two compression options: 50% and 60%. Compressing files to a smaller size reduces the amount of data transmitted over the network, which can be beneficial in terms of speed and resource utilization. Understanding and optimizing these parameters is crucial for effective data communication.

Bandwidth Calculation

Bandwidth is the maximum rate at which data can be transmitted over a network connection, usually measured in megabytes per second (MB/sec) or megabits per second (Mbps).
In the exercise, we calculated the bandwidth at which the total time for compressing and transferring a file would be the same for two different compression options.
Here's how we solved it:
- For 50% compression, the file size becomes 0.5 MB. The time taken for compression is 1 second, and the transmission time is \(\frac{0.5}{B}\). So, the total time is 1 + \(\frac{0.5}{B}\) seconds.
- For 60% compression, the file size is reduced to 0.4 MB. The time taken for compression is 2 seconds, and the transmission time is \(\frac{0.4}{B}\). Thus, the total time is 2 + \(\frac{0.4}{B}\) seconds.
By setting the total times equal, we get the equation:
\[ 1 + \frac{0.5}{B} = 2 + \frac{0.4}{B} \]
Solving this, we find that the bandwidth \( B \) is 0.1 MB/sec.
This calculation helps us understand how changing compression and transmission rates impacts overall file transfer efficiency.

Latency in Networks

Latency refers to the delay between the sender sending a packet of data and the receiver receiving it. It's measured in milliseconds (ms). High latency can negatively impact the speed of data transmission, making real-time applications, like video calls or online gaming, challenging.
However, in the context of our exercise, latency doesn't affect the result as it remains constant for both compression options. Latency only adds a fixed delay, independent of file size or bandwidth.
For instance, if the network latency is 100 ms, this delay will be the same whether the file is 0.5 MB or 0.4 MB. Hence, when comparing the total times for different compression methods, the latency cancels out.
Understanding the concept of latency helps us design and manage networks more effectively, ensuring that data transfer is as efficient as possible.