Calculate Transmission and Propagation Delays in Networks

This problem requires us to calculate two important types of delays in a network: transmission delay and propagation delay. These delays are fundamental concepts in understanding network performance and throughput.

Understanding Network Delays

In data communication, when a frame or packet is sent from one point to another, it experiences various delays. Two primary delays are:

• Transmission Delay ($\text{T}_\text{r}$): The time taken to push all the bits of a frame onto the transmission medium. It depends on the frame size and the bandwidth (data rate) of the link.
• Propagation Delay ($\text{T}_\text{p}$): The time it takes for a bit to travel from the sender to the receiver. It depends on the distance between the sender and the receiver and the propagation speed of the signal in the medium.

Calculating Transmission Delay ($\text{T}_\text{r}$)

The transmission delay is calculated using the formula:

$\text{T}_\text{r} = \frac{\text{Frame Size}}{\text{Bandwidth}}$

From the problem description, we have:

• Frame size = 64 bytes
• Bandwidth = 1.536 Mbps

First, we need to ensure the units are consistent. Let's convert the frame size to bits and the bandwidth to bits per second.

• Frame size in bits = 64 bytes $\times$ 8 bits/byte = 512 bits
• Bandwidth in bits/sec = 1.536 Mbps = $1.536 \times 10^6$ bits/sec

Now, calculate the transmission delay:

$\text{T}_\text{r} = \frac{512 \text{ bits}}{1.536 \times 10^6 \text{ bits/sec}}$

$\text{T}_\text{r} = \frac{512}{1536000} \text{ seconds}$

To express this in microseconds ($\mu$sec), we multiply by $10^6$:

$\text{T}_\text{r} = \frac{512}{1536000} \times 10^6 \mu\text{sec}$

$\text{T}_\text{r} = \frac{512000000}{1536000} \mu\text{sec}$

$\text{T}_\text{r} = \frac{512000}{1536} \mu\text{sec}$

$\text{T}_\text{r} = 333.333... \mu\text{sec}$

Rounding to two decimal places, we get $\text{T}_\text{r} \approx 333.33 \mu\text{sec}$.

Calculating Propagation Delay ($\text{T}_\text{p}$)

The propagation delay is calculated using the formula:

$\text{T}_\text{p} = \text{Distance} \times \text{Propagation Speed}$

From the problem description, we have:

• Distance = 3000 km
• Propagation speed = 6 $\mu$sec/km

Now, calculate the propagation delay:

$\text{T}_\text{p} = 3000 \text{ km} \times 6 \mu\text{sec/km}$

$\text{T}_\text{p} = 18000 \mu\text{sec}$

Summary of Calculated Delays

Our calculated values are:

• Transmission Delay ($\text{T}_\text{r}$) $\approx 333.33 \mu\text{sec}$
• Propagation Delay ($\text{T}_\text{p}$) $= 18000 \mu\text{sec}$

Comparing with Options

Let's compare our calculated values with the given options:

Our calculated values for transmission delay (approximately 333.33 $\mu$sec) and propagation delay (18000 $\mu$sec) match Option 1.

Revision Table: Key Network Delay Formulas

Additional Information: Factors Affecting Network Delays

Besides transmission and propagation delays, other factors contribute to the total delay experienced by data in a network:

• Queuing Delay: Time a packet spends waiting in router queues. This delay is variable and depends on network congestion.
• Processing Delay: Time taken by routers to process packet headers, check for errors, and determine the output link.

The sliding window protocol mentioned in the problem primarily affects the efficiency of data transfer by controlling the number of frames that can be sent without waiting for acknowledgements, but the fundamental transmission and propagation delays for each frame remain calculated as shown above.