# Q1C · ALOHA throughput

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/mocks/tee-mock-c/q1c

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/mocks/tee-mock-c--q1c/

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



$$
S=G e^{-2G}
$$



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



$$
e^{-1.6} \approx 0.201896518
$$



#### 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.

#### What this result means

A computed throughput at the given G is not automatically the maximum. Increasing attempts beyond the optimum produces more collisions.