You are tasked with designing a scalable Distributed Rate Limiter to protect a high-traffic API ecosystem. The system must support thousands of microservices across multiple geographical regions (e.g., US-East, EU-West) and handle a peak load of 1 million requests per second.

Requirements:

1. Accuracy: The solution must ensure that a user cannot exceed their defined quota (e.g., 100 requests per minute) regardless of which server or region processes the request.
2. Low Latency: The rate-limiting check must add less than 5ms of overhead to the total request processing time.
3. Resiliency: If the rate-limiting service or the underlying data store (e.g., Redis) becomes unavailable, the system should fail open to allow traffic rather than blocking all users.
4. Efficiency: Minimize the "thundering herd" problem and network overhead caused by frequent synchronization between regions.

Question: Which algorithm (Leaky Bucket, Token Bucket, or Sliding Window Log) would you choose and why? Describe your data consistency strategy and how you would minimize cross-region latency while maintaining a global count.