Entanglement routing in a first-generation quantum network must decide, jointly, which path carries each source–destination (S–D) request and how many purification rounds are performed on every link of that path, because entanglement swapping degrades fidelity while purification restores it at the cost of additional raw Bell pairs drawn from finite link capacity. Existing fidelity-guaranteed designs solve one request at a time and then allocate capacity to the resulting paths sequentially, in the order of a heuristic utility, so an allocation made for one request ignores its effect on requests not yet served. We formulate the multi-request problem as a path-based integer linear program (ILP) that selects routes and integer Bell-pair allocations for all S–D pairs simultaneously under shared link-capacity constraints. The multiplicative end-to-end fidelity requirement is removed from the program by precomputing, for each candidate route, the minimum-cost purification vector with a label-setting dynamic program in the log-fidelity domain. On the 39-node US backbone topology, and against faithful reimplementations of the two reference algorithms, the joint formulation raises delivered throughput by 1.7%–10.0%, with the largest gains where link capacity is scarce or request load is high. The gain is obtained at a higher raw-pair consumption per delivered qubit, which we quantify

Quantum networks,entanglement routing,entanglement purification,integer linear programming,multi-commodity flow,resource allocation