  We investigate resource allocation for quantum entanglement distribution over
an optical network. We characterize and model a network architecture that
employs a single quasi-deterministic time-frequency heralded
Einstein-Podolsky-Rosen (EPR) pair source, and develop a routing scheme for
distributing entangled photon pairs over such a network. We focus on max-min
fairness in entanglement distribution and compare the performance of various
spectrum allocation schemes by examining the max-min and median number of
EPR-pairs assigned by them, and the Jain index associated with this assignment.
Since this presents an NP-hard problem, we identify two approximation
algorithms that outperform others in minimum and mean EPR-pair rate
distribution and are comparable to others in the Jain index. We also analyze
how the network size and connectivity affect these metrics using Watts-Strogatz
random graphs. We find that a spectrum allocation approach that achieves high
minimum EPR-pair rate can perform significantly worse when the median EPR-pair
rate, Jain index, and runtimes are considered.
