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FAA's NextGen program aims at increasing the capacity of the national airspace, while ensuring the safety of aircraft. This paper provides a distributed merging and spacing algorithm that maximizes the throughput at the terminal phase of flight using the information provided through the ADS-B framework. Using dual decomposition, aircraft negotiate with each other and reach an agreement on optimal merging times, with respect to an associated cost, that ensures proper inter-aircraft spacing. We provide a feasibility analysis that gives sufficient conditions to guarantee that proper spacing is achievable and derive maximum throughput controllers based on the air traffic characteristics of the merging flight paths.