Solution

The correct answer is 1.691726 s.

Explanation:

To determine the total delay (latency) for the frame size of 10 million bits, we will consider transmission delay, propagation delay, queuing delay, and processing delay. Let's break it down step-by-step.

Given Data:

• Frame size: 10 million bits (10⁷ bits)
• Number of routers: 20
• Queuing time per router: 2 μs (2 × 10^-6 s)
• Processing time per router: 1 μs (1 × 10^-6 s)
• Length of the link: 5000 km (5 × 10⁶ m)
• Speed of light inside the link: 2 × 10⁸ m/s
• Link bandwidth: 6 Mbps (6 × 10⁶ bits/s)

Steps to Calculate Delay:
Transmission Delay: [\( \text{Transmission Delay} = \frac{\text{Frame Size}}{\text{Link Bandwidth}} ] [ \text{Transmission Delay} = \frac{10^7 \text{ bits}}{6 \times 10^6 \text{ bits/s}} = \frac{10}{6} \text{ seconds} \approx 1.6667 \text{ seconds}\)

Propagation Delay: \(\text{Propagation Delay} = \frac{\text{Length of Link}}{\text{Speed of Light in the Medium}} ] [ \text{Propagation Delay} = \frac{5 \times 10^6 \text{ m}}{2 \times 10^8 \text{ m/s}} = 0.025 \text{ seconds}\)

Queuing Delay per Router:

• \(\text{Total Queuing Delay} = \text{Number of Routers} \times \text{Queuing Time per Router}\)
• \(\text{Total Queuing Delay} = 20 \times 2 \times 10^{-6} \text{ s} = 40 \times 10^{-6} \text{ s} = 40 \text{ μs} = 0.00004 \text{ s}\)

Processing Delay per Router:

• \(\text{Total Processing Delay} = \text{Number of Routers} \times \text{Processing Time per Router}\)
• \(\text{Total Processing Delay} = 20 \times 1 \times 10^{-6} \text{ s} = 20 \times 10^{-6} \text{ s} = 20 \text{ μs} = 0.00002 \text{ s}\)

Total Delay:

• \( \text{Total Delay} = \text{Transmission Delay} + \text{Propagation Delay} + \text{Total Queuing Delay} + \text{Total Processing Delay}\)
• \( \text{Total Delay} = 1.6667 \text{ s} + 0.025 \text{ s} + 0.00004 \text{ s} + 0.00002 \text{ s} = 1.69176 \text{ s} \)

Upon reviewing the answer choices, it is closest to: 2) 1.691726 s

Therefore, the total delay for the frame is approximately 1.691726 seconds.