Occupancies

Occupancy denotes the state of being occupied or the number of people occupying a space at a given time. The plural occupancies is used when discussing multiple spaces or time periods.

In combinatorics, the occupancy problem studies distributing objects into containers and tracking which containers are occupied. Occupancy numbers describe the counts in each container and are modeled by distributions such as the multinomial; many questions ask the probability that a given number of containers are nonempty.

In building design and safety, occupancy relates to occupant load—the expected or measured number of people in a space. Codes set maximum occupancies to ensure safe egress and adequate ventilation. Different space types carry distinct load factors, and accurate occupancies influence fire protection, crowd management, and ventilation requirements.

In real estate and hospitality, occupancy rate is the proportion of available units or rooms that are in use. Occupancy statistics inform pricing, revenue management, and performance evaluation, as well as planning for maintenance and services.

In smart buildings and facility management, occupancy sensing uses sensors and data to infer presence and adjust lighting, heating, cooling, and ventilation. Occupancy data may be anonymized and analyzed to improve energy efficiency, indoor air quality, and occupant comfort while supporting safety and analytics.