Disaggregated LLM inference forces the KV cache to traverse the datacenter network before decoding begins, so transfer time enters directly into the Time to First Token (TTFT) budget. Current schedulers route on compute load and prefix-cache locality alone, ignoring the topological distance and dynamic congestion between prefill and decode instances. We close this gap with a thin operator-to-scheduler interface, the network cost oracle, and we prove that ignoring the network term renders cache-aware-only scheduling arbitrarily suboptimal as context length grows. NetKV, the O(|D|) per-request greedy that consumes this oracle, has tier rankings that are provably robust to stale telemetry. On a 64-GPU four-tier fat-tree simulator driven by Mooncake traces, NetKV reduces mean TTFT by up to 21.2% over round-robin and 17.6% over a tuned cache+load-aware scheduler, lifts SLO attainment by up to 20.1 percentage points, and keeps the Time Between Tokens overhead below 0.5 ms in every condition tested, with no changes to the transport, inference engine, or hardware.

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