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How long does it take a packet of length 1,000 bytes to propagate over a link of distance \(2,500 \mathrm{~km}\), propagation speed \(2.5 \cdot 10^{8} \mathrm{~m} / \mathrm{s}\), and transmission rate 2 Mbps? More generally, how long does it take a packet of length \(L\) to propagate over a link of distance \(d\), propagation speed \(s\), and transmission rate \(R\) bps? Does this delay depend on packet length? Does this delay depend on transmission rate?

Short Answer

Expert verified
Propagation delay is 0.01 seconds and depends only on distance and speed, not packet length or transmission rate.

Step by step solution

01

Understanding Propagation Delay

Propagation delay is the time it takes for a signal to propagate from the sender to the receiver over a specific distance with a given speed. It is calculated using the formula \( \text{Propagation Delay} = \frac{d}{s} \), where \(d\) is the distance and \(s\) is the propagation speed.
02

Calculate Propagation Delay for Given Values

Substitute the given values into the propagation delay formula. Here, \(d = 2500 \times 10^3 \) meters and \(s = 2.5 \times 10^8 \) m/s, so: \[ \text{Propagation Delay} = \frac{2500 \times 10^3}{2.5 \times 10^8} = 0.01 \text{ seconds} \]
03

Understand Impact of Packet Length and Transmission Rate

Propagation delay depends solely on the distance and propagation speed, not on the packet length \(L\) or the transmission rate \(R\). Therefore, when calculating propagation delay, we do not consider these.
04

Answer General Question About Propagation Delay Dependency

The propagation delay \( \frac{d}{s} \) depends only on the distance \(d\) and the propagation speed \(s\). It does not depend on the packet length \(L\) or the transmission rate \(R\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Packet Length
Packet length refers to the size or amount of data that is packed into one unit, often measured in bytes. In computer networks, the packet length can affect how data is sent and processed. A packet has a header and data payload, where the length of the payload determines the total packet length.
They vary depending on the protocol used and the amount of information sent. In our example, the packet length is 1,000 bytes. Understanding packet length is important because in a network, a larger packet might take longer to transmit, depending on the transmission rate.
While packet length is vital for determining transmission time, it doesn't affect propagation delay. Propagation delay is purely a function of physical distance and speed, as the delay is governed by how fast the signal travels through the medium.
Transmission Rate
Transmission rate, or bandwidth, is the rate at which data is transmitted over a network. It is mainly measured in bits per second (bps). In our case, the transmission rate is 2 Mbps (Megabits per second). This is a critical factor in determining how quickly one packet can be sent from the source to the destination.
The transmission rate indicates how much data can travel across the network in one second:
  • If the transmission rate is high, data can be sent faster.
  • If it's lower, more time is required to send the same amount of data.
However, it's important to note that the transmission rate impacts the overall time to send the packet, not the propagation delay. Propagation delay is unaffected by how fast data is being sent once the transmission is complete.
Propagation Speed
Propagation speed is the speed at which the signal travels through the medium (like wire or cable). Its value depends on the type of material used and the signal characteristics. In our exercise, the propagation speed is given as \(2.5 \times 10^8 \) meters per second, which is a typical value close to the speed of light.
The propagation speed is crucial for determining the propagation delay, calculated as the distance divided by the speed. For example:
  • Faster propagation speeds lead to shorter delays.
  • Slower speeds result in longer delays.
It is important to remember that propagation speed impacts only the time it takes for the signal to travel the distance, not how long it takes to transmit the data OVER that distance.
Distance
Distance in networking context refers to the physical space the signal must cover from sender to receiver. It is often measured in kilometers, meters, or miles. In our scenario, the distance is 2,500 km. This concept heavily influences propagation delay, as the signal must physically traverse this space.
The relationship between distance and propagation delay is direct:
  • The longer the distance, the greater the propagation delay.
  • Shorter distances translate to reduced delay times.
Understanding this concept is important, especially when planning network topologies. Networks with long-range communication will experience longer delay times simply due to the increased distances involved. This is crucial for applications requiring real-time data transmission.

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Most popular questions from this chapter

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 \(100 \mathrm{kbps}\).

(a) Visit the site www.traceroute.org and perform traceroutes from two different cities in France to the same destination host in the United States. How many links are the same in the two traceroutes? Is the transatlantic link the same? (b) Repeat (a) but this time choose one city in France and another city in Germany. (c) Pick a city in the United States, and perform traceroutes to two hosts, each in a different city in China. How many links are common in the two traceroutes? Do the two traceroutes diverge before reaching China?

Consider sending a large file of \(F\) bits from Host A to Host B. There are three links (and two switches) between \(A\) and \(B\), and the links are uncongested (that is, no queuing delays). Host A segments the file into segments of \(S\) bits each and adds 80 bits of header to each segment, forming packets of \(L=80+S\) bits. Each link has a transmission rate of \(R\) bps. Find the value of \(S\) that minimizes the delay of moving the file from Host A to Host B. Disregard propagation delay.

This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, A and B, connected by a single link of rate \(R\) bps. Suppose that the two hosts are separated by \(m\) meters, and suppose the propagation speed along the link is \(s\) meters/sec. Host A is to send a packet of size \(L\) bits to Host B. a. Express the propagation delay, \(d_{\text {prop }}\), in terms of \(m\) and \(s\). b. Determine the transmission time of the packet, \(d_{\text {trans }}\), in terms of \(L\) and \(R\). c. Ignoring processing and queuing delays, obtain an expression for the endto- end delay. d. Suppose Host A begins to transmit the packet at time \(t=0\). At time \(t=d_{\text {trans }}\). where is the last bit of the packet? e. Suppose \(d_{\text {prop }}\) is greater than \(d_{\text {trans }} .\) At time \(t=d_{\text {trans }}\), where is the first bit of the packet? f. Suppose \(d_{\text {prop }}\) is less than \(d_{\text {trans }} .\) At time \(t=d_{\text {trans }}\), where is the first bit of the packet? g. Suppose \(s=2.5 \cdot 10^{8}, L=120\) bits, and \(R=56 \mathrm{kbps}\). Find the distance \(m\) so that \(d_{\text {prop }}\) equals \(d_{\text {trans }}^{-}\)

Suppose you would like to urgently deliver 40 terabytes data from Boston to Los Angeles. You have available a 100 Mbps dedicated link for data transfer. Would you prefer to transmit the data via this link or instead use FedEx overnight delivery? Explain.

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