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Three methods for modeling allocation of water rights under different types of water rights systems are presented. The priority-based maximal multiperiod network flow (PMMNF) programming method searches for optimal allocations over the whole river basin and multiple periods, strictly preserving priority order by sequential programming. PMMNF is a flexible method that can be applied under prior, riparian and public water regimes with priorities determined by different criteria. The modified riparian water rights allocation (MRWRA) approach for water allocation under a riparian rights system is a special form of PMMNF, which assigns senior priorities to the basic water demands of all riparian landowners and junior priorities to their surplus demands. MRWRA recognizes that, an upstream riparian has the privilege to take water but should constrain its diversions for surplus demands to meet the basic needs of downstream riparian demands. The lexicographic minimax water shortage ratios method is a technique for water allocation under a public water rights regime adopting the lexicographic minimax fairness concept, which interprets fairness as minimizing weighted water shortage ratios of all water uses and the differences among them. The weights can be set based on the “equivalent weighted water shortage ratios” rule. The proposed methods may also be applied to international basins as long as water demands and associated priorities or weights are selected to reflect relevant international water allocation principles and agreements. These approaches and their algorithms are evaluated using an illustrative application to the Amu Darya River Basin located within the Aral Sea Basin of Central Asia. [ABSTRACT FROM AUTHOR]