Computer Networks · M2 · papers

Q1C · Pure ALOHA throughput

Re-exam · 4 February 2026

Actual TEE paper · current-M2 matching parts; original marks

Actual PYQ. In a Pure ALOHA system, the average number of frames generated per frame time is G = 0.5. Calculate the throughput S. What is the maximum possible throughput in Pure ALOHA? [5 marks]

Answer

Given

Protocol = Pure ALOHA; G = 0.5 attempts/frame time.

To find

S, 100S and the maximum possible S.

Formula and why

S=G e^{-2G}LaTeX: S=G e^{-2G}

Select the formula from the protocol name. The exponent is −2G because Pure ALOHA has a 2T vulnerable period.

Step-by-step solution

Step 1. Calculate the exponent

−2 × 0.5 = -1.

Step 2. Evaluate the exponential

e^{-1} \approx 0.367879441LaTeX: e^{-1} \approx 0.367879441

Step 3. Multiply by G

S = 0.5 × 0.367879441 ≈ 0.183939721 successful frames/frame time.

Step 4. Convert to percentage

0.183939721 × 100 ≈ 18.3940%.

Step 5. State the maximum separately

The maximum is 1/(2e) ≈ 0.183940 = 18.3940%, at G=0.5.

Final answer: S ≈ 0.183940; percentage ≈ 18.3940%; Smax ≈ 0.183940 at G=0.5.