GATE CS 2017 Set 2 Q35 — Transport Layer: Flow Control, Congestion Control, UDP, TCP, Sockets

To find the transmission delay ($p$) and propagation delay ($q$), we use their standard definitions:

1. Transmission Delay ($p$)

Transmission delay is the time taken to push all the packet's bits into the link.

$$\text{Transmission Delay } (p) = \frac{\text{Message Size (in bits)}}{\text{Transmission Rate (Bandwidth)}}$$

Given:

• Message Size = $50,000 \text{ bytes} = 50,000 \times 8 \text{ bits} = 400,000 \text{ bits}$
• Transmission Rate = $10^6 \text{ bits/sec}$

$$p = \frac{400,000 \text{ bits}}{10^6 \text{ bits/sec}} = 0.4 \text{ seconds} = 400 \text{ milliseconds}$$

2. Propagation Delay ($q$)

Propagation delay is the time taken for the first bit of the message to travel from the sender to the receiver.

$$\text{Propagation Delay } (q) = \frac{\text{Distance}}{\text{Propagation Speed}}$$

Given:

• Distance = $10,000 \text{ km} = 10^7 \text{ meters}$
• Propagation Speed = $2 \times 10^8 \text{ meters/sec}$

$$q = \frac{10^7 \text{ m}}{2 \times 10^8 \text{ m/sec}} = 0.05 \text{ seconds} = 50 \text{ milliseconds}$$

Thus, $p = 400$ and $q = 50$, which matches Option D.