Question

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

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

Step-by-step solution

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.

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: \[ \text{Propagation Delay} = \frac{2500 \times 10^3}{2.5 \times 10^8} = 0.01 \text{ seconds} \]

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.

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 \(R\).

Key concepts

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.