Design Google Calendar

Design a scalable Google Calendar service that supports personal and enterprise users. The system must handle recurring events using RRULE (RFC 5545), time-zone-aware scheduling, free/busy queries, reminders, and mobile/offline sync. Requirements: (1) Support 100M daily-active users, 1B events, 500M reminders/day, 50k free/busy QPS. (2) Recurring events: store once with RRULE, expand on read; allow exceptions for individual occurrences. (3) Free/busy: return user availability in <100ms; pre-compute daily busy intervals. (4) Reminders: deliver email/push notifications within ±5s of scheduled time. (5) Time zones: events created in any zone, displayed correctly in viewer’s zone; handle DST transitions. (6) Sharing & permissions: user can share calendar read-only or read-write; enterprise policies restrict visibility. (7) Mobile sync: incremental sync with change tokens; support offline edits that merge on reconnect. (8) Availability: 99.99% uptime; regional failover in <30s. Provide high-level architecture, data models, APIs, and scaling strategies for each component.