Modeling regular occupancy in commercial buildings using stochastic models

Buildings account for some 40% of the world's total energy usage. One factor that could help to improve energy efficiency in buildings is more accurate modeling of occupancy. In this paper, we propose two novel stochastic inhomogeneous Markov chains to model building occupancy under two scenarios of multi-occupant single-zone (MOSZ) and multi-occupant multi-zone (MOMZ) respectively. In the MOSZ scenario, instead of using occupancy (i.e. the number of occupants in a zone) as the state, we define the state of the inhomogeneous Markov chain as the increment of occupancy in the zone. In the MOMZ scenario, by taking into account interactions among zones, we propose another inhomogeneous Markov chain whose state is a vector in which each component represents the increment of occupancy in each zone. In this way, we can significantly simplify the calculation of transition probability matrix which is a key parameter in Markov chain models. Several simulations with real data have been conducted to evaluate the performance of the proposed models under the two scenarios. To quantify the performance of the proposed models, five variables related to occupancy properties and two evaluation criteria are defined. The results show that our proposed approaches have superior performance over existing ones.