Before revision:  For long-run fairness, we analyze two online algorithms (sampling and pooling ) which establish asymptotic optimality across many different regimes (no specialized supplies, no rare demand types, or imbalanced supply/demand).
After revision:  For long-run fairness, we propose two online heuristics (Sampling and Pooling ) which establish asymptotic optimality across many different regimes (no specialized supplies, no rare demand types, or imbalanced supply/demand).