# Q1C · Slotted ALOHA

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/papers/tee-paper-final/q1c

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/papers/tee-paper-final--q1c/

TEE · Actual TEE paper · all questions · current syllabus 702AI0C023

### Actual PYQ · Q1C. In a Slotted ALOHA system, the average number of frames generated per frame time is G = 1. Calculate the throughput S. What is the maximum throughput in Slotted ALOHA? [5 marks]

#### Answer

## Given

Protocol = Slotted ALOHA; G = 1 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 × 1 = -1.

#### Step 2. Evaluate the exponential



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



#### Step 3. Multiply by G

S = 1 × 0.367879441 ≈ 0.367879441 successful frames/frame time.

#### Step 4. Convert to percentage

0.367879441 × 100 ≈ 36.7879%.

#### Step 5. State the maximum separately

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

**Final answer:** S ≈ 0.367879; percentage ≈ 36.7879%; 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.

Source: Final · 5 December 2025, original question paper page 1. Original marks retained; solution independently authored.