Design a scalable game matchmaking and waiting-queue system

Context

You are designing the matchmaking system for a large real-time multiplayer game. Players join a waiting queue and are matched into games under constraints such as team size, region, and skill level.

Tasks

1. Overall architecture: components, data flow, and interactions from Join Queue to Game Start.
2. Data model: entities, required fields, indexes, and storage choices.
3. Matchmaking algorithm: queueing model, candidate selection, scoring, and formation of matches.
4. Fairness and low wait times: policies and mechanisms to balance match quality vs. latency.
5. Timeouts, cancellations, retries: ready-check flow, heartbeats, and requeue logic.
6. Constraints: team size, region and latency, skill level, parties; how they are enforced and relaxed.
7. High concurrency: sharding strategy, worker assignment, and hot-spot mitigation.
8. Reliability: idempotency, failure recovery, backpressure, and observability.

Assume a global player base with multiple regions, multiple game modes (e.g., 1v1, 3v3, 5v5), and peak spikes. Target low wait times and high match quality.