Device B is trying to transmit a data frame of size 2000 bytes in a wireless network using CSMA/CA with binary exponential backoff. The data rate is 2 Mbps, and the slot time is 20 microseconds. The DIFS (Distributed Inter-Frame Space) is 45 microseconds, and the SIFS (Short Inter-Frame Space) is 26 microseconds. The CW (Contention Window) size is 32, and the ACK frame size is 27 bytes. Device B has to wait for the average backoff time before each transmission attempt. What is the average total time (in microseconds) taken for Device B to successfully transmit the data frame, assuming there are no collisions? Round off your answer to the nearest whole number.

Question

BlackTom AI · Accepted Answer

Average backoff (in slots) = (CW − 1)/2, so average backoff time = 15.5 slots × 20 μs/slot = 310 μs.

1) Relevant concepts
- CSMA/CA transmission sequence (when medium is idle): wait DIFS → random backoff → DATA transmission → wait SIFS → ACK transmission.
- Average backoff for a uniformly chosen slot in [0, CW−1] is (CW−1)/2 slots.
- Frame transmission time = (frame size in bits) / data rate.

2) Step-by-step reasoning and calculations
- Contention Window (CW) = 32 slots, so average backoff slots = (32 − 1)/2 = 31/2 = 15.5 slots.
- Slot time = 20 μs, so average backoff time = 15.5 × 20 μs = 310 μs.

- DATA frame size = 2000 bytes = 2000 × 8 = 16,000 bits.
- DATA transmission time = 16,000 bits / 2,000,000 bits/s = 0.008 s = 8,000 μs.

- ACK frame size = 27 bytes = 27 × 8 = 216 bits.
- ACK transmission time = 216 bits / 2,000,000 bits/s = 0.000108 s = 108 μs.

- Fixed inter-frame spaces: DIFS = 45 μs, SIFS = 26 μs.

3) Sum all components (no collisions assumed)
Total time = DIFS + average backoff + DATA_tx + SIFS + ACK_tx
= 45 μs + 310 μs + 8,000 μs + 26 μs + 108 μs
= 8,489 μs

4) Why this answer is correct
This follows the CSMA/CA timing order and uses the correct average backoff formula for a uniform choice from 0 to CW−1. All frame durations computed by converting bytes to bits and dividing by the given physical data rate.

5) Common incorrect approaches (brief)
- Using CW/2 instead of (CW−1)/2 yields 320 μs for backoff and would give 8,499 μs (slightly off).
- Omitting DIFS or SIFS or forgetting to convert bytes→bits would undercount the total.

Conclusion: The computed average total time is 8,489 microseconds, matching the provided answer 8489.

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