Question

Calculate the bandwidth \(x\) delay product for the following links. Use one-way delay, measured from first bit sent to first bit received. (a) 10-Mbps Ethernet with a delay of \(10 \mu \mathrm{s}\). (b) 10-Mbps Ethernet with a single store-and-forward switch like that of Exercise \(18(\mathrm{a})\), packet size 5000 bits, and \(10 \mu\) ser link propagation delay. (c) \(1.5\)-Mbps T1 link, with a transcontinental one-way delay of \(50 \mathrm{~ms}\). (d) \(1.5-\mathrm{Mbps} \mathrm{T} 1\) link through a satellite in geosynchronous orbit, \(35,900 \mathrm{~km}\) high. The only delay is speed-of- light propagation delay.

Short answer

100 bits, 200 bits, 75,000 bits, and 179,505 bits.

Step-by-step solution

Understanding the Bandwidth-Delay Product Formula

The bandwidth-delay product is calculated using the formula: \[ \text{Bandwidth-Delay Product} = \text{Bandwidth} \times \text{Delay} \] This gives the amount of data that can be in transit in the network.

Calculate Bandwidth-Delay Product for 10-Mbps Ethernet with a Delay of 10 μs

Here, \( \text{Bandwidth} = 10 \text{ Mbps} \) \( \text{Delay} = 10 \text{ μs} = 10 \times 10^{-6} \text{ s} \) Using the formula: \[ \text{Bandwidth-Delay Product} = 10 \times 10^6 \text{ bits/s} \times 10 \times 10^{-6} \text{ s} = 100 \text{ bits} \]

Calculate Bandwidth-Delay Product for 10-Mbps Ethernet with a Single Store-and-Forward Switch

Here, the total delay is the sum of the propagation delays for the two links. \( \text{Total Delay} = 10 \text{ μs} + 10 \text{ μs} = 20 \text{ μs} = 20 \times 10^{-6} \text{ s} \) \( \text{Bandwidth} = 10 \text{ Mbps} \)Using the formula: \[ \text{Bandwidth-Delay Product} = 10 \times 10^6 \text{ bits/s} \times 20 \times 10^{-6} \text{ s} = 200 \text{ bits} \]

Calculate Bandwidth-Delay Product for 1.5-Mbps T1 Link with Transcontinental One-Way Delay

Here, \( \text{Bandwidth} = 1.5 \text{ Mbps} \) \( \text{Delay} = 50 \text{ ms} = 50 \times 10^{-3} \text{ s} \) Using the formula: \[ \text{Bandwidth-Delay Product} = 1.5 \times 10^6 \text{ bits/s} \times 50 \times 10^{-3} \text{ s} = 75,000 \text{ bits} \]

Calculate Bandwidth-Delay Product for 1.5-Mbps T1 Link through a Satellite

\( \text{Delay} = 0.11967 \text{ s} \) \( \text{Bandwidth} = 1.5 \text{ Mbps} \) Using the formula: \[ \text{Bandwidth-Delay Product} = 1.5 \times 10^6 \text{ bits/s} \times 0.11967 \text{ s} = 179,505 \text{ bits} \]

Key concepts

network bandwidth

Network bandwidth is the rate at which data is transmitted over a network channel. We often measure it in bits per second (bps), such as Mbps (megabits per second) or Gbps (gigabits per second).
For example, a 10-Mbps Ethernet connection can transmit 10 million bits per second.
Network bandwidth is crucial because it determines the data transfer speed and affects network performance. Higher bandwidth means faster data transfer.

• In practical terms, think of bandwidth as the width of a highway. The wider the highway, the more cars (data) can travel at once.
• If you're streaming video, playing online games, or making video calls, ample bandwidth ensures a smooth experience without buffering or lag.

propagation delay

Propagation delay refers to the time it takes for a signal to travel from the sender to the receiver over a network medium.
This delay is influenced by the speed of light, the distance between the sender and receiver, and the type of medium (e.g., fiber optic, copper cable).
For instance, the propagation delay in a 10-Mbps Ethernet with a delay of 10 μs means it takes 10 microseconds for the first bit to reach the destination.

• It's like sending a message with a carrier pigeon over a certain distance; the further the distance, the longer it takes for the pigeon to deliver the message.
• In satellite communications, the propagation delay is notably high due to the vast distance signals must travel to and from space.

store-and-forward switching

Store-and-forward switching is a method where a network switch receives the entire data packet before forwarding it to the next device.
This method ensures that error checking can be done—if there's an error, the packet is discarded.
In a 10-Mbps Ethernet with a switch and packet size of 5000 bits and 10 μs link propagation delay, the switch needs to add its delay to the transmission time.
Store-and-forward adds an extra step but increases reliability by minimizing the chances of corrupted packets spreading further.

• Imagine a relay race where each runner waits to receive the baton fully before starting the next segment. This ensures smooth passing of data.
• Although it adds delay, error checking makes it beneficial for networks where data integrity is critical.

T1 link

A T1 link is a type of network connection providing a data rate of 1.5 Mbps. It is commonly used in businesses and telecommunication infrastructures.
The T1 link can carry voice and data transmission, making it versatile for various applications.
When considering the bandwidth-delay product, like in a transcontinental T1 link, you find that it's reasonably significant due to the longer delays involved.
For a 50 ms one-way delay, the T1 link's bandwidth-delay product will be 75,000 bits, indicating how much data can be in transit.

• Imagine T1 links as dedicated pipelines for data, ensuring a steady and reliable flow.
• Even though 1.5 Mbps might seem slow compared to modern internet speeds, T1 links provide dedicated bandwidth which can be critical for specific use cases.

satellite communication

Satellite communication involves transmitting data between earth stations through satellites in space. These satellites can be in geostationary orbit, meaning they stay fixed relative to a point on Earth.
Due to the distance (around 35,900 km for geostationary satellites), the propagation delay is quite large—approximately 0.11967 seconds.
This delay affects the bandwidth-delay product significantly. For a 1.5-Mbps T1 link, the delay results in a high bandwidth-delay product, showing a substantial amount of data in transit.

• Think of satellite communication like sending data on a very long relay race with a baton passing many checkpoints.
• The high delay in satellite communication can impact applications requiring real-time interaction, such as online gaming or VoIP.