We propose a novel stochastic agent-based model of occupancy dynamics in a building with an arbitrary number of zones and occupants. Simulation of the model yields time-series of the location of each agent (a software representation of an occupant). The model is meant to provide realistic simulation of occupancy dynamics in nonemergency situations. Comparison of the model's prediction of distributions of random variables such as first arrival time of a building is provided against those estimated from measurements in commercial buildings. We also propose a lower complexity graphical model of occupancy evolution in multi-zone buildings. The graphical model captures information on mean occupancy and correlation among occupancy at various zones in the building. The agent-based model can be used in conjunction with building performance simulation tools, while the graphical model is more suitable for real-time applications, such as occupancy estimation with noisy sensor measurements.

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We examine distributed time-synchronization in mobile ad-hoc and sensor networks. The problem is to estimate the skews and offsets of clocks of all the nodes with respect to an arbitrary reference clock. Pairs of nodes that can communicate with each other can obtain noisy measurements of the relative skews and offsets between them. We propose a distributed algorithm with which each node can estimate its offset/skew from these noisy relative measurements by communicating only with its neighbors. The algorithm is simple and easy to implement. We model the change in the communication network due to the moving nodes as a Markov chain whose state space is the set of graphs that can occur. Using tools from Markov Jump Linear Systems, we provide a sufficient condition for the mean square convergence of the estimation error. A conjecture on mean square convergence under weaker conditions is discussed. Monte Carlo simulations are provided that corroborate the predictions and justify the conjecture.