Model specification: Advertised-service serial repeater model

Fix a finite lattice graph.

1. Each edge has one positive service duration ${\tau }_e$, sampled independently from $\mathrm{Exp}(\lambda )$ and advertised to the route controller independently of the message.

2. When activated, the edge service prepares a perfect Bell pair after exactly ${\tau }_e$ time units.

3. Quantum memories are perfect. Bell measurements, Pauli corrections, and the classical messages needed for those corrections have zero duration in this ideal timing contract.

4. The controller chooses a route before dispatch, using the advertised durations. Along that route, service is activated only after the message has arrived at the preceding vertex.

5. All Bell outcomes and all surviving registers are included in the complete protocol specification. No successful branch alone is treated as a deterministic channel.

This is an externally timed service model, not a derivation of physical link-generation statistics or an optimal concurrent repeater protocol.