# Q1C · ALOHA throughput

Subject: Computer Networks

Exam: TEE

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

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

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

### TEE practice mock · Q1C. In a Slotted ALOHA system, the offered load is G=0.6. Find normalized throughput, percentage throughput, and the theoretical maximum. [5 mock marks]

#### Answer

## Given

Protocol = Slotted ALOHA; G = 0.6 attempts/frame time.

## To find

S, 100S and the maximum possible S.

## Formula and why



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



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

## Step-by-step solution

#### Step 1. Calculate the exponent

−1 × 0.6 = -0.6.

#### Step 2. Evaluate the exponential



$$
e^{-0.6} \approx 0.548811636
$$



#### Step 3. Multiply by G

S = 0.6 × 0.548811636 ≈ 0.329286982 successful frames/frame time.

#### Step 4. Convert to percentage

0.329286982 × 100 ≈ 32.9287%.

#### Step 5. State the maximum separately

The maximum is 1/(1e) ≈ 0.367879 = 36.7879%, at G=1.

**Final answer:** S ≈ 0.329287; percentage ≈ 32.9287%; Smax ≈ 0.367879 at G=1.

#### What this result means

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