Consider a network using the pure ALOHA medium access control protocol, where…
2021
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 (=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 ______________ .
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Correct answer: 135
Key formula: For pure ALOHA the throughput in frames per frame time is S' = G'·e^{-2G'}, where G' is the offered load in frames per frame time.
Step 1: Compute the frame transmission time T = frame size / channel rate = 1000 bits / 10^6 bits/s = 0.001 s.
Step 2: Compute the normalized offered load G' = aggregate attempt rate × T = 1000 frames/s × 0.001 s = 1.
Step 3: Compute throughput per frame time S' = G'·e^{-2G'} = 1·e^{-2} ≈ 0.135335.
Step 4: Convert to frames per second: S = S' / T = 0.135335 / 0.001 ≈ 135.335 frames/s, which rounds to 135 frames per second.
Final answer: The throughput of the network (rounded to the nearest integer) is 135 frames per second.
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