A slotted ALOHA network transmits 200 bits frames using a shared channel with…
2016
A slotted ALOHA network transmits 200 bits frames using a shared channel with 200 kbps bandwidth. If the system (all stations put together) produces 1000 frames per second, then the throughput of the system is _______.
- A.
0.268
- B.
0.468
- C.
0.368
- D.
0.568
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Correct answer: C
Key formula: throughput for slotted ALOHA is S = G · e^{−G}
Find frame transmission time: frame size / bandwidth = 200 bits / 200000 bits/s = 0.001 s (1 ms).
Slots per second = 1 / frame time = 1 / 0.001 s = 1000 slots/s.
Offered traffic G = frames generated per second ÷ slots per second = 1000 ÷ 1000 = 1.
Compute throughput: S = G · e^{−G} = 1 · e^{−1} = 1/e ≈ 0.367879 ≈ 0.368.
Interpreting the result: the normalized throughput is about 0.368, which means roughly 0.368 successful transmissions per slot. With 1000 slots per second this corresponds to about 368 successful frames per second.