Question

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 \(d_{\text {trans }}^{-}\)

Short answer

The distance \( m \) is approximately 5,357.14 meters for equal propagation and transmission delays.

Step-by-step solution

Calculate Propagation Delay

The propagation delay \( d_{\text{prop}} \) is the time it takes for a signal to travel from Host A to Host B through the link. Given that the propagation speed is \( s \) meters/second and the distance between the hosts is \( m \) meters, the propagation delay can be expressed as: \[ d_{\text{prop}} = \frac{m}{s} \]

Calculate Transmission Delay

The transmission delay \( d_{\text{trans}} \) is the time required to push all the packet bits into the link. Given the packet size \( L \) in bits and the link transmission rate \( R \) in bits per second, the transmission delay is: \[ d_{\text{trans}} = \frac{L}{R} \]

Calculate End-to-End Delay

The end-to-end delay, ignoring processing and queuing delays, is the sum of the propagation delay and the transmission delay. Thus, it is expressed as: \[ d_{\text{end-to-end}} = d_{\text{prop}} + d_{\text{trans}} = \frac{m}{s} + \frac{L}{R} \]

Determine Location of Last Bit at Transmission Time

At time \( t = d_{\text{trans}} \), the last bit has just been transmitted from Host A and is entering the link. Therefore, it is at the start of the link, right at Host A.

Determine Location of First Bit When \( d_{\text{prop}} > d_{\text{trans}} \)

If the propagation delay is greater than the transmission delay, at time \( t = d_{\text{trans}} \), the first bit is still in transit on the link but has not yet reached Host B. It is at a distance of \( t \times s \) from Host A.

Determine Location of First Bit When \( d_{\text{prop}} < d_{\text{trans}} \)

If the propagation delay is less than the transmission delay, at time \( t = d_{\text{trans}} \), the first bit has already arrived at Host B.

Find Distance for Equal Delays

To find the distance \( m \) so that \( d_{\text{prop}} = d_{\text{trans}} \), set \( \frac{m}{s} = \frac{L}{R} \) and solve for \( m \). Given \( s = 2.5 \times 10^8 \) m/s, \( L = 120 \) bits, and \( R = 56,000 \) bps, we have: \[ m = \frac{L}{R} \times s = \frac{120}{56,000} \times 2.5 \times 10^8 \] Calculating gives \( m \approx 5,357.14 \) meters.

Key concepts

End-to-End Delay

In the world of computer networks, the term "end-to-end delay" is crucial. It refers to the total time taken for a packet of data to travel from the source to the destination across a network. This delay is a combination of various types of delays, but the two primary ones are propagation delay and transmission delay.

Propagation delay is the time it takes for a single bit to travel through the medium from one end of the transmission link to the other. It's driven by the physical distance between the two points and the speed at which the signal travels. On the other hand, transmission delay is the time it takes to place all bits of a packet onto the wire. This depends on the packet size and the network bandwidth or transmission rate.

To calculate end-to-end delay, you sum up these two components, assuming no other delays like processing or queuing are involved. The formula can be expressed as:

• Propagation Delay: \( d_{\text{prop}} = \frac{m}{s} \)
• Transmission Delay: \( d_{\text{trans}} = \frac{L}{R} \)
• End-to-End Delay: \( d_{\text{end-to-end}} = d_{\text{prop}} + d_{\text{trans}} \)

Understanding this relationship helps in network delay analysis and optimization, ensuring efficient data transfer across networks.

Packet Transmission

Packet transmission in networking involves sending packets of data from one host to another over a network link. This process is pivotal as it affects how quickly and reliably data can be sent and received, impacting overall network performance.

When transmitting a packet, the data is broken down into smaller packets. Each packet then traverses the network by following a specific path from the source to the destination. The effectiveness of packet transmission depends largely on the transmission delay, which is the time required to send all packet bits into the link. This is determined by both the size of the packet and the bandwidth of the transmission medium. The formula for transmission delay is:

• Transmission Delay: \( d_{\text{trans}} = \frac{L}{R} \)

It's important in network delay analysis to consider how packets are managed and transmitted, as it directly influences the end-to-end delay and the speed of communication within the network.

Network Delay Analysis

Network delay analysis is a critical part of understanding how networks perform. This involves examining the delays that occur as data is transmitted across the network. Network delay consists of several components, each contributing to the total time it takes for data to travel from the sender to the receiver.

Besides transmission and propagation delays, network delay analysis typically also considers processing delay, which is the time taken by routers to process packet headers, and queuing delay which is the wait time a packet experiences in router input and output queues. When focusing on the basic concepts, we often evaluate:

• Transmission Delay
• Propagation Delay
• End-to-End Delay

By conducting a thorough network delay analysis, network architects can identify bottlenecks and optimize network settings to ensure that data flows smoothly, enhancing overall network performance and reliability.