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GATE CSE 2021 Set 2 Q64: Pure ALOHA throughput at 1000 frames/s on a 1 Mbps channel

Question

Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps (=106= 10^6 bits per second). The aggregate number of transmissions across all the nodes (including new frame transmissions and retransmitted frames due to collisions) is modelled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is ________.

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 130 to 140 (official GATE 2021 final answer key)

Concept used: Pure ALOHA success probability is e−2Ge^{-2G}, where GG is the offered load per frame time.

First step: Frame time is 1 ms, so G=1000×10−3=1G = 1000 \times 10^{-3} = 1; throughput =1000⋅e−2G= 1000 \cdot e^{-2G} frames per second.

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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