# Random Walk and Lighting Control

We pose the problem of turning off a single luminaire (or group) as an optimal stopping problem. We present the stationary and first-passage analysis of motion data obtained using custom wireless nodes in an open office floor plan. These calculations allow us to estimate the state of the network and calculate the probability and expected number of steps to visit a state from any arbitrary state. We also investigate if there is any evidence of clustering amongst the nodes by studying the covariance of the dataset. The data indicate the existence of clustering within the lattice. In other words, the analysis of random walk prevents luminaires from accidentally shutting off and dimensionality reduction determines the correct zoning of lighting via the occupants' movements.