Video Processing: Simulate a Multi-Stage Video Transcoding Pipeline

Question

## Problem

You are building a simplified video processing pipeline. Each uploaded video must go through three sequential stages: `INGEST -> TRANSCODE -> PUBLISH`. Each stage takes a fixed number of time units.

Given a list of videos with their arrival times and per-stage durations, simulate the pipeline and return the completion time for each video. Assume a single worker per stage and a FIFO queue.

```python
from typing import List, Tuple

def simulate_pipeline(
    arrivals: List[Tuple[str, int]],
    stage_durations: Tuple[int, int, int]
) -> List[Tuple[str, int]]:
    # arrivals: [(video_id, arrival_time), ...] sorted by arrival_time
    # stage_durations: (ingest_time, transcode_time, publish_time)
    # return: [(video_id, finish_time), ...]
    pass
```

**Example:**
```
arrivals = [("v1", 0), ("v2", 2)]
stage_durations = (3, 5, 2)

v1: ingest 0-3, transcode 3-8, publish 8-10  -> finish=10
v2: ingest 3-6, transcode 8-13, publish 13-15 -> finish=15

Output: [("v1", 10), ("v2", 15)]
```

## Follow-ups

1. How does your simulation change if you have 3 parallel transcode workers?
2. What data structure gives you O(log n) scheduling if priorities vary by video resolution?
3. In a real distributed system, how would you track stage state durably so a worker crash doesn't lose progress?
4. How would you model re-try logic if a stage fails with a 10% probability?

Video Processing: Simulate a Multi-Stage Video Transcoding Pipeline

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