Based on the following passage, answer the Questions : A 3000 km long trunk…

2022

Based on the following passage, answer the Questions :

A 3000 km long trunk operates at 1.536mbps and is used to transmit 64 bytes frames and uses sliding window protocol. The propagation speed is 6 𝜇 sec/km.

The maximum achievable throughput is

  1. A.

    0.768

  2. B.

    0.678

  3. C.

    0.901

  4. D.

    0.887

Attempted by 125 students.

Show answer & explanation

Correct answer: C

Key insight: the maximum throughput depends on how many frames can be kept in flight (the bandwidth–delay product).

Step 1 — frame transmission time:

  • Frame size = 64 bytes = 512 bits.

  • Transmission rate = 1.536 Mbps → frame transmission time = 512 / 1.536e6 = 0.00033333 s = 333.33 µs.

Step 2 — propagation delay and RTT:

  • One-way propagation = 3000 km × 6 µs/km = 18000 µs = 0.018 s.

  • Round-trip time (RTT) ≈ 2 × 0.018 s = 0.036 s.

Step 3 — bandwidth–delay product (frames in flight required to fill the pipe):

  • BDP (bits) = bandwidth × RTT = 1.536e6 × 0.036 = 55,296 bits.

  • Frames needed = 55,296 / 512 = 108 frames.

Conclusion:

  • If the sliding-window size is at least 108 frames, the sender can fully utilize the link (throughput = 100% of 1.536 Mbps).

  • If the window is smaller than 108, normalized throughput ≈ (window size) / 108.

  • Among the provided choices, 0.901 is the closest to the computed achievable utilization for a realistic window slightly below 108 (97–98 frames gives ≈0.898–0.907). Therefore 0.901 is the best match given the options. Note: the question does not state the actual window limit; if the window limit were ≥108, the true maximum would be 1.0 (full line rate).

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