fragmentation

Before vLLM, engines reserved the maximum context for every request up front and wasted most of it. The fix borrowed virtual memory from the operating system, and the numbers show how much capacity it returned.

Fractions are either hardware slices with fixed shapes or soft shares with no isolation, and the scheduler has to know which. The representation, the packing score, the fragmentation arithmetic that spread placement produces, and the defragmentation step that fixes it.

Allocated is not usable: a cluster full of half-empty nodes has hundreds of idle GPUs that no gang can take. The arithmetic of how mixed job sizes fragment a fleet, the packing policies that prevent it, the defragmentation moves that repair it, and what each costs the jobs already running.

Free GPUs and a pending gang are not a contradiction: the gang needs 64 whole nodes at once and the free GPUs sit on 300 half-used nodes. The isolation order (quota, fit, per-node reasons, one node's device plugin), the command at each step and what it means, and the fixes ranked by displacement.

Three one-line policy differences produce different fragmentation, and the metric that separates them is not utilization. The measured outcome on the same job sequence, why the largest free block is what matters on a training cluster, and the case where the intuitive policy is exactly wrong.