Bounded Blocking Buffer with Shutdown and Timeouts

You are asked to design and implement a thread-safe, fixed-capacity producer–consumer buffer that supports multiple producers and consumers.

Functional Requirements

• FIFO ordering of items.
• Configurable capacity N.
• put(item):
  • Blocks when the buffer is full.
  • A timed put(item, timeout) variant that times out if space does not become available in time.
• take():
  • Blocks when the buffer is empty.
  • A timed take(timeout) variant that times out if no item becomes available in time.
• shutdown():
  • Unblocks any waiting producers/consumers.
  • Rejects new puts after shutdown is invoked.
  • After shutdown, consumers may still take remaining items; if the buffer is empty, take should not block.

Non-Functional and Correctness Requirements

• Thread-safe for multiple producers and consumers.
• Prevent race conditions, deadlocks, and lost wakeups.
• Discuss fairness and performance trade-offs.
• Analyze time and space complexity.
• If time permits: compare a lock-based design (mutex + condition variables) to a lock-free approach.

Assume a Java-like API and execution model (mutex/condition variables, interrupts, and timed waits). You may use a circular array for FIFO ordering.