ATC Sectors, Capacity, and Altitude Bands

Model an ATC sector as the Cartesian product of a 2D footprint and an altitude band. Compute the instantaneous count of aircraft against the sector's Monitor Alert Parameter (MAP) to detect overload. Extend the model to vertical stacks of sectors sharing a footprint, and combine altitude-band filtering with peak-count analysis.

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Tutorial

Sectors as Footprint × Altitude Band

An ATC sector is a three-dimensional volume of airspace managed by a single controller (or controller team). Each sector is built from two pieces:

a footprint $F$ — a 2D polygon from the planar partition of the airspace, and
an altitude band $[h_{lo}, h_{hi})$ — a vertical slab of flight levels.

The sector itself is the Cartesian product

S \;=\; F \times [h_{lo}, h_{hi}).

A flight at position $(x, y, h)$ is inside sector $S$ if and only if

(x, y) \in F \quad \text{and} \quad h_{lo} \le h < h_{hi}.

The upper boundary is open by convention: a flight at exactly $h = h_{hi}$ belongs to the sector stacked immediately above $S$ , not to $S$ itself.

For example, suppose $F = \{(x,y) : 0 \le x \le 50,\; 0 \le y \le 30\}$ (nautical miles) and the band is $[\text{FL}240, \text{FL}340)$ . A flight at $(20, 15, \text{FL}310)$ is in $S$ because $0 \le 20 \le 50$ , $0 \le 15 \le 30$ , and $240 \le 310 < 340$ . A flight at $(20, 15, \text{FL}340)$ is not in $S$ , since $340 \not< 340$ .