To solve this, we need to equate the propagation delay and the transmit delay for different packet sizes.

Step 1: Propagation delay (T_prop)

The propagation delay is the time it takes for a signal to travel through the medium from the sender to the receiver.

$T_{prop} = \frac{d}{v}$

where:

• $d = 4 \, \text{km} = 4000 \, \text{m}$ (the distance of the link),
• $v = 2 \times 10^8 \, \text{m/s}$ (the propagation speed).

$T_{prop} = \frac{4000}{2 \times 10^8} = 2 \times 10^{-5} \, \text{seconds} = 20 \, \mu s$

Step 2: Transmit delay (T_trans)

The transmit delay is the time it takes to put all the bits of the packet onto the wire.

$T_{trans} = \frac{L}{B}$

where:

• $L$ is the size of the packet in bits,
• $B$ is the bandwidth in bits per second (bps).

Step 3: Equating the propagation delay and transmit delay

We want to find the bandwidth $B$ where $T_{prop} = T_{trans}$.

$T_{prop} = \frac{L}{B}$

$B = \frac{L}{T_{prop}}$

Case 1: For 100-byte packets

• $L = 100 \, \text{bytes} = 100 \times 8 = 800 \, \text{bits}$,
• $T_{prop} = 20 \, \mu s = 20 \times 10^{-6} \, \text{seconds}$.

$B = \frac{800}{20 \times 10^{-6}} = 40 \times 10^6 \, \text{bps} = 40 \, \text{Mbps}$

Case 2: For 512-byte packets

• $L = 512 \, \text{bytes} = 512 \times 8 = 4096 \, \text{bits}$,
• $T_{prop} = 20 \, \mu s$.

$B = \frac{4096}{20 \times 10^{-6}} = 204.8 \times 10^6 \, \text{bps} = 204.8 \, \text{Mbps}$

Final Results:

• For 100-byte packets, the required bandwidth is 40 Mbps.
• For 512-byte packets, the required bandwidth is 204.8 Mbps.

Let me know if you need more details or have any questions!

Here are 5 related questions to deepen understanding:

1. How would propagation delay change if the distance were halved?
2. What happens to the transmit delay if packet size increases but bandwidth remains the same?
3. How do different packet sizes affect overall latency on a network?
4. What is the impact of higher bandwidth on the transmission delay for small packets?
5. How does the speed of light in fiber optics compare to the given propagation speed?

Tip: Bandwidth affects how quickly data can be transmitted, but propagation delay depends solely on the distance and medium speed!