LLM Request Batching System

Implement a request batching system for LLM API calls to optimize throughput and costs.

## Requirements
{{batching_requirements}}

## Current Traffic Pattern
{{traffic_pattern}}

## Latency Constraints
- Max batch wait time: {{max_wait_ms}}ms
- Target batch size: {{target_batch_size}}

Implement a complete solution:

```python
class LLMBatcher:
    """
    Implement:
    - Dynamic batch sizing
    - Timeout-based flushing
    - Priority queue support
    - Error handling per request
    - Metrics collection
    """
```

Include:
- Thread-safe implementation
- Async/await support
- Backpressure handling
- Unit tests