Thirty years of modeling midair collisions

For 30 years, operations researchers have developed mathematical models of processes leading to possible collisions of aircraft flying in proximity to one another in order to estimate the risk of collision. These ‘collision risk models’ were applied in the 1960s to determine safe separation standards between pairs of co-altitude aircraft on parallel courses over the North Atlantic Ocean. The models have been and are being continually refined and improved. They have been applied to different geographic regions (for example, the Pacific Ocean and domestic airspace), to different flight regimes (for example, high-altitude cruise and landing on closely spaced runways), and to different types of separation (vertical and longitudinal as well as lateral).