Question

Suppose Host A wants to send a large file to Host B. The path from Host A to Host B has three links, of rates \(R_{1}=500 \mathrm{kbps}, R_{2}=2 \mathrm{Mbps}\), and \(R_{3}=1 \mathrm{Mbps}\). a. Assuming no other traffic in the network, what is the throughput for the file transfer? b. Suppose the file is 4 million bytes. Dividing the file size by the throughput, roughly how long will it take to transfer the file to Host B? c. Repeat (a) and (b), but now with \(R_{2}\) reduced to \(100 \mathrm{kbps}\).

Short answer

(a) Throughput is 500 kbps. (b) Transfer time is 64 seconds. (c) With reduced \(R_2\), throughput is 100 kbps and transfer time is 320 seconds.

Step-by-step solution

Identify the Bottleneck Link

In a network path, the throughput is constrained by the link with the smallest transmission rate. Thus, examine the rates: \(R_1 = 500 \text{ kbps}, R_2 = 2 \text{ Mbps}, R_3 = 1 \text{ Mbps}\). The bottleneck link is \(R_1 = 500 \text{ kbps}\), which is the smallest rate among the links.

Calculate the Throughput for Part (a)

For part (a), since \(R_1\) is the bottleneck, the throughput is \(500 \text{ kbps}\). This means that data can be transferred at this rate along the entire path because \(R_2\) and \(R_3\) can handle more data than \(R_1\) can pass through.

Convert File Size for Calculation

The file size given is 4 million bytes. Convert this to bits for consistency with the throughput rate: \(4,000,000 \text{ bytes} \times 8 = 32,000,000 \text{ bits}.\)

Calculate Transfer Time for Part (b)

To find the transfer time, divide the file size in bits by the throughput: \[\text{Transfer Time} = \frac{32,000,000 \text{ bits}}{500,000 \text{ bits per second}} = 64 \text{ seconds}.\]

Adjust Network for New Conditions

For part (c), reduce \(R_2\) to \(100 \text{ kbps}.\) Re-evaluate the network to find the new bottleneck, which is now \(R_2 = 100 \text{ kbps}\), smaller than \(R_1\) and \(R_3\).

Calculate Throughput for Adjusted Network

Under the new condition, the throughput is \(100 \text{ kbps}\) since \(R_2\) is now the bottleneck.

Recalculate Transfer Time for Part (c)

With the new bottleneck, recalculate the transfer time:\[\text{Transfer Time} = \frac{32,000,000 \text{ bits}}{100,000 \text{ bits per second}} = 320 \text{ seconds}.\]

Key concepts

Bottleneck Link

In any network path, the concept of a bottleneck link is crucial as it determines the maximum throughput achievable along that path. Let's think of each link as a pipe carrying data. The link with the smallest bandwidth, or transmission rate, acts like the narrowest pipe in a series, restricting the flow no matter how wide the other pipes are.
For example, given three links with rates of 500 kbps, 2 Mbps, and 1 Mbps, the smallest rate is the bottleneck. Here, 500 kbps on the first link confines the data flow, even though the subsequent links can handle higher rates. Changing the network could change the bottleneck. It depends on the comparative rates of each link in the network path.

File Transfer Time

File transfer time is a critical metric for understanding how long it will take to move data from one host to another over a network. It is essentially the time required to transmit all packets of a file across the network path.

• First, convert the file size into bits (since transmission rates are in bits per second). For instance, a 4 million byte file equates to 32 million bits.
• To find the transfer time, divide the total number of bits by the network throughput, which, due to the bottleneck link, is the minimum transmission rate.

In our example, with a throughput of 500 kbps, the time needed is 64 seconds. If a link's rate decreases, as in reducing the second link to 100 kbps, it becomes the new bottleneck and the transfer time increases to 320 seconds.

Transmission Rate

The transmission rate of a network link is its capacity to pass data, typically given in bits per second (bps). This rate can be thought of as how fast you can pour data into the link, analogous to how much water a pipe can carry in a given amount of time.
The rate is pivotal in determining the overall efficiency of information flow in a network. For our case:

• Link 1 has a rate of 500 kbps.
• Link 2 originally at 2 Mbps.
• Link 3 at 1 Mbps.

Reduction in the transmission rate of any link can lead to a new bottleneck, such as lowering Link 2 to 100 kbps. Each link's rate directly influences both throughput and thus, transfer time.

Network Path

A network path is the route data takes from one host to another, passing through various interconnected links or nodes. It is crucial for understanding the potential delays and capacity limitations occurring during data transfer.
The path's performance is determined by several factors, but notably:

• The number of links within the path.
• The transmission rate of each link on that path.

In scenarios where no other network traffic exists, the path's throughput matches the rate of the slowest link. This indicates that the path's efficiency and overall transfer speed rely heavily on the link with the least capacity—again, the bottleneck.