Distributed Priority Job Scheduler with Lock Leasing & Dead-Letter Queue

### Problem Overview Enterprise async job pipelines (Temporal, BullMQ, Celery, SQS) orchestrate millions of concurrent background tasks across distributed worker nodes. Build a **Priority Job Scheduler** in TypeScript supporting priority ordering, worker lock leases with heartbeat renewals, automatic failure backoff, and dead-letter queue (DLQ) routing. ### Functional Requirements 1. **Priority Scheduling**: - Enqueue jobs with numeric priority (`priority: number`), delay (`delayMs?: number`), and max retries (`maxRetries: number`). 2. **Worker Lock Leasing (At-Least-Once Execution)**: - When a worker leases a job (`leaseJob(workerId: string, leaseDurationMs: number)`), the job becomes invisible to other workers. - If the worker crashes or fails to renew its lease before expiry, the scheduler makes the job available again. 3. **Heartbeat Lease Renewal**: - `renewLease(jobId: string, workerId: string, extensionMs: number): boolean`. 4. **Exponential Retries & Dead Letter Queue (DLQ)**: - If a job fails or times out, retry up to `maxRetries` with exponential backoff. - When retries are exhausted (poison pill), move job to the Dead-Letter Queue with error logs. 5. **Job Metrics & Observability**: - `getStats(): { pending: number; active: number; completed: number; failed: number; dlq: number }`. ### Non-Functional Requirements - **High Concurrency**: Queue extraction must be (O(\log N)). - **Fault Tolerance**: Prevent zombie jobs from locking the scheduler indefinitely.