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Recently, there has been considerable research on using mobility in wireless sensor and actor networks (WSANs) to assist in the deployment of nodes and meet the sensing, communication, and actuation coverage requirements. One of the well-know simulators used to evaluate the performance of wireless sensor networks is TOSSIM. It has the advantage that its code can also run in real systems, and hence it allows better comparison between experimental and simulation results. However, it is designed to simulate only static sensor networks. In this paper, we propose a classification scheme that categorizes the mobility models in WSANs. Based on this classification, we design and implement MOB-TOSSIM, the first extension framework to TOSSIM that supports mobility in WSNs and WSANs. MOB-TOSSIM implements three components: (1) a set of probabilistic and controlled mobility models, (2) an extended and modified version of Power TOSSIM that includes the energy consumption due to mobility and radio transmission, and (3) a radio component based on a realistic propagation model. Experiment results show that MOB-TOSSIM is scalable with respect to network size and node speed, as it incurs an acceptable additional execution time compared to TOSSIM.