As serving capacity demand surpasses that of training, serving efficiency becomes increasingly important. Prefill-decode (P/D) disaggregation improves serving efficiency through specialization and isolation of the two phases. These benefits rest on a static partitioning. Phase demand, however, is not static. We observe that in a large LLM fleet the ratio of uncached input to output tokens has peak-to-mean ratios up to 4.7x at minute timescales, and that in a public agentic trace the hourly ratio spans a median 24.5x within a single day, while reassigning a replica takes tens of minutes. Agentic traffic sharpens the mismatch. Sizing each pool at its ninety-fifth percentile leaves up to 17% of cluster capacity unused; sizing below it converts the same imbalance into queueing and unrealized throughput. We present Crossflow, which makes this boundary elastic without changing node roles. Each decode node publishes a short-lived, revocable lease that bounds local-prefill compute, KV capacity, transfer work, and projected output. Across public and internal traces, Crossflow improves token throughput by 16.2-17.4% on geometric mean over static P/D, and by up to 43.4% at high load, while reducing mean TTFT at every evaluated point.

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