Belegungsfunktion

Belegungsfunktion is a term used in German-speaking technical literature to describe a function that depicts the occupancy state or occupancy level of a resource over time. It maps time (or a time index) to a value that indicates how much of the resource is used.

In discrete form, Belegungsfunktion B(t) may take values 0 or 1, indicating that a single unit is free or occupied at time t. In aggregated or fractional form, B(t) ∈ [0,1] can represent the fraction of a set of identical units that are occupied at time t, i.e., the occupancy rate or utilization.

Applications include facility management and logistics (room or machine occupancy, parking space usage, warehouse slot filling), data centers and computing (memory or CPU occupancy as a function of time and workload), and transport or healthcare sectors where occupancy informs capacity planning, staffing, and scheduling.

Properties of a Belegungsfunktion can vary: it may be time-varying, piecewise constant, or stochastic. It is often derived from arrival and service processes; in steady state, the long-run occupancy level relates to the utilization factor ρ = arrival rate / service rate. Estimation uses historical data, time-series methods, or queueing models, and projections can be made under different scenario assumptions.

The concept is related to terms such as utilization, occupancy probability, and occupancy rate. The exact interpretation depends on the domain and whether the focus is on instantaneous state (binary) or average occupancy over a period.