# Q3(a) · Store-and-forward caravan

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/papers/paper-2024-ai-final/q3a

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/papers/paper-2024-ai-final--q3a/

Exact historical variant. Current-syllabus questions solved; excluded topics and source limitations stated.

### Q3(a). Ten cars queue at a tollbooth; service is one car per second. Each road to the next booth is 400 km; speed is 10 km/s. A booth waits for the entire caravan before servicing its first car. Find: (1) one-car service time; (2) whole-caravan service time; (3) first car travel time after departure; (4) last car travel time after departure; (5) time from first departure to its next service; (6) whether first and second booths ever service cars simultaneously; (7) whether there is an interval with neither servicing any car. [10 marks]

### Answer

### Given

10 cars; service1car/s; road400km; speed10km/s; each booth waits for all10 cars.

### To find

All seven timing/overlap questions.

### Formula and why



$$
T_{service}=N/r,\quad T_{travel}=d/v
$$



Transmission corresponds to serializing the whole caravan; propagation is the road journey of each individual car.

### Solution

### Step 1. Choose t=0 as first service start

Car1 leaves at1s; car10 leaves at10s. Travel=400/10=40s. Thus first arrival at booth2 is41s and last arrival is50s. Booth2 starts service only at50s.

### Step 2. Answer every printed subpart

| Part | Answer | Reason |
| --- | --- | --- |
| 1 | 1 second | One car per second |
| 2 | 10 seconds | 10/1 |
| 3 | 40 seconds | Measured from first car departure |
| 4 | 40 seconds | Last car travels the same road at the same speed |
| 5 | 49 seconds | From first departure t1 to next service t50:50−1 |
| 6 | No | First booth service0–10; second50–60 |
| 7 | Yes | Neither is servicing during(10,50); in particular before first arrival, (10,41) |

Common mistake: part5 is not50s because its clock starts when the first car leaves, one second after the first service began.