Contents I. Introduction
This work aims to quantify the maximum capacity of a sector (in the National Airspace System, NAS) and to develop an automation procedure that achieves the maximum sector capacity. It is noted that sector capacity is used for planning and execution of Air Traffic Management (ATM). For example, capacity is used for flow planning at the national and regional level to avoid overloads and to reduce wasted resource [1]. The sector capacity is also used, along with demand forecasting methods, to optimize Air Traffic Control (ATC) and Airline Operations Center decisions [2]. While the acceptable input-flow-rate of a single aircraft route can be quantified based on minimum separation requirements [3], it is difficult to quantify the acceptable input-flow-rates for multiple intersecting routes because the conflict resolution procedures used at the intersections generates interference between aircraft flows in the different routes. However, a conservative upper bound on the acceptable, total input-flow-rates into a sector can be established by using the maximum, acceptable output-flow-rate of the sector. This upper bound on the total input-flow-rates guarantees that aircraft and delays do not accumulate in the sector. In particular, to avoid accumulation, the sum of all the input-flow-rates of all routes which exit the sector at a particular output (see Figure 1) should not exceed the acceptable output-flow-rate , i.e., satisfies the {Accumulation \ Constraint}: \sum\limits_{i,k=j}\lambda(R_{i,k})\leq\bar{\lambda}(O_{j}).\eqno{\hbox{(1)}}
