Expiry Certified Cluster Routing for Renewable Key Pools in Trusted Relay QKD Networks

Finite key storage, continuous key generation, and expiring service commitments jointly determine whether a trusted relay quantum key distribution network can sustain an additional key service. Inventory and generation metrics alone do not characterize this duration dependent admission capacity. We introduce expiry certified routing (ECR), which derives an admissible rate from the cumulative obligations of each link and uses that rate for both admission and path selection. Its central analytical result is a finite event certificate: under constant floor generation, reserve feasibility over the entire remaining service interval is equivalent to inequalities at commitment expiration events. Repeated admission preserves the reserve invariant under online arrivals. We establish feasible set inclusion relative to a fixed horizon approximation, characterize monotonicity and reservation updates, and prove that an all-gateway cluster representation preserves the minimum feasible routing cost. A paired evaluation uses three synthetic network families, 30 seeds, and heterogeneous decoy state BB84 reference rates. At nominal load 1.4, ECR improves completed key service over fixed horizon headroom routing by 13.6–30.4%, while its gain over the strongest certificate matched routing control is 0.8–2.1%. Independently formulated single link linear programs and gateway graph comparisons agree with the analytical reductions to numerical precision.