# Q1C · Pure ALOHA throughput

Subject: Computer Networks

Exam: M2

Reader: https://deep-learning-study-room.vercel.app/cn/#m2/papers/paper-2026-reexam/q1c

Canonical: https://deep-learning-study-room.vercel.app/read/cn/m2/papers/paper-2026-reexam--q1c/

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



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



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



$$
e^{-1} \approx 0.367879441
$$



#### 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.

#### What this result means

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