Edge platforms instantiate executable services close to users to reduce request-serving cost, but each instance incurs a one-time deployment cost and remains useful only for a finite time-to-live (TTL). The resulting online decision is both prediction-sensitive and capacity-coupled: an optimistic forecast can waste deployment cost, whereas a delayed decision misses the burst it is intended to serve. We study this problem under a common TTL cost model and propose CAPSUM, a capacity-aware admission policy with an elastic specialization, CAPSUM-E. In the local elastic setting, every node-service trace is exactly a variable-price Bahncard instance. This reduction lets CAPSUM-E inherit PFSUM's tight prediction-error-dependent ratio, including $2/(1+β)$ consistency and $1/β$ robustness for $β>0$. A redirect-aware variant preserves the same local deployment schedule. For finite-capacity nodes, CAPSUM combines size-scaled break-even tests, a utilization-dependent shadow price, and evidence-density eviction; we prove capacity feasibility, scale invariance, and exact agreement with CAPSUM-E under an elastic configuration. We implement an exact local offline dynamic program and compare against direct common-model baselines and documented source-derived adapters for EDP-A, OREO, and uEDC-L. Experiments cover controlled prediction error, three synthetic demand regimes, a causal predictor on a public Globus Compute trace, and joint scaling to 1,024 nodes and 10,000 services. Under the common model, CAPSUM reduces normalized cost by 33.7-42.9% relative to the best source-derived adapter across the synthetic regimes and by 45.5% on the sampled trace.

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