Computer Networks · TEE · mocks

Q1C · ALOHA throughput

TEE mock C · full paper

TEE · 100 attempted marks · solutions for every choice · current syllabus 702AI0C023

TEE practice mock · Q1C. In a Pure ALOHA system, the offered load is G=0.8. Find normalized throughput, percentage throughput, and the theoretical maximum. [5 mock marks]

Answer

Given

Protocol = Pure ALOHA; G = 0.8 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 × 0.8 = -1.6.

Step 2. Evaluate the exponential

e^{-1.6} \approx 0.201896518LaTeX: e^{-1.6} \approx 0.201896518

Step 3. Multiply by G

S = 0.8 × 0.201896518 ≈ 0.161517214 successful frames/frame time.

Step 4. Convert to percentage

0.161517214 × 100 ≈ 16.1517%.

Step 5. State the maximum separately

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

Final answer: S ≈ 0.161517; percentage ≈ 16.1517%; Smax ≈ 0.183940 at G=0.5.