Continuous Batching or PagedAttention — Which Fixes This Symptom?

A team running a self-hosted model behind a naive request-at-a-time serving setup observes two separate symptoms under real concurrent load: (1) GPU utilization graphs show clear idle gaps even while requests are queued waiting to be served, and (2) the serving process occasionally fails to accept a new request with an out-of-memory error, even though the sum of currently active requests' actual token counts so far is well under the GPU's KV-cache capacity.

1. Which of vLLM's two core techniques addresses symptom (1), and explain the mechanism that causes the idle gaps in the first place.
2. Which technique addresses symptom (2), and explain why the OOM happens despite actual token usage being well under capacity.
3. Would adopting only one of the two techniques (not both) fully resolve this team's problems? Explain why or why not.