Design a distributed system for a ride-hailing service that can handle millions of requests per day, with features such as real-time ride tracking, payment processing, and fraud detection.

When responding to this question, begin by illustrating a high-level architecture that can handle the specified requirements and scale. Discuss utilizing a microservices architecture to promote scalability and maintainability. Elaborate on how you would implement real-time ride tracking, likely via gps and map services, and consider discussing the integration of external payment gateways for processing payments securely. Address the implementation of robust fraud detection mechanisms, potentially leveraging machine learning models, to identify and prevent fraudulent activities. Discuss the application of load balancing, data partitioning, and replication to manage the millions of requests efficiently. Don’t forget to mention any relevant databases, caching strategies, and data indexing you would use to ensure data integrity and fast data retrieval. It's crucial to demonstrate your understanding of designing scalable distributed systems that can cater to real-time needs and high demand, focusing on balancing performance, security, and reliability throughout the conversation.