```python
from typing import Callable, Dict, Any

class JobQueue:
    def __init__(self):
        self.jobs: Dict[str, Dict[str, Any]] = {}

    def add_job(self, job_id: str, payload: Dict[str, Any]) -> None:
        self.jobs[job_id] = {
            "payload": payload,
            "status": "pending",
            "retry_count": 0,
            "next_backoff": 0.0
        }

    def process_job(self, job_id: str, processor: Callable) -> bool:
        job = self.jobs.get(job_id)
        if not job:
            return False

        max_retries = 3
        for attempt in range(max_retries + 1):
            try:
                processor(job["payload"])
                job["status"] = "completed"
                return True
            except Exception:
                job["retry_count"] = attempt + 1
                if job["retry_count"] <= max_retries:
                    job["next_backoff"] = 2 ** (job["retry_count"] - 1)
                else:
                    job["status"] = "failed"
                    return False
        return False
```