How does Kafka's TimingWheel work and why is it used in Purgatory?

Kafka's Purgatory uses a hierarchical TimingWheel data structure (inspired by the paper 'Hashed and Hierarchical Timing Wheels') for efficient deferred operations. A TimingWheel is a circular buffer of buckets where each bucket represents a time slot. When a task's deadline approaches, it cascades from higher-level to lower-level wheels for finer granularity. This enables O(1) insert and O(1) expire operations (vs O(log n) for a heap-based delayed queue). It's used for expiring Produce Requests waiting for ISR acks and Fetch Requests waiting for min.fetch.bytes accumulation.

Expected key concepts: TimingWheel, hierarchical, circular buffer, buckets, cascade, O(1) insert, O(1) expire, heap, Purgatory, deferred operations, min.fetch.bytes