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In this work, a novel two-dimensional (2-D) random-walk mobility model is proposed, which can be used for studying and analyzing the location-area crossing rate and dwell time of mobile users in wireless networks. The development and application of the model under two cell structures, namely the square and hexagon cells, have been detailed. The analytical results obtained for location-update rates and dwell times have been validated using simulated and published results. The highlights of the model are its simplicity, minimal assumptions, and adaptability to conduct both "location-crossing rate" and "dwell-time" studies using the same model with slight modifications for either the square or hexagon cells. Using symmetry of mobile-user movement, a reduced number of computational states was achieved. A novel wrap-around feature of the model facilitates reduced assumptions on user mobility, which has also resulted in considerably reduced mathematical computation complexity. A regular Markov chain model was used for computing the average location-area crossing rate. A slightly modified model with absorbing states was used to derive the dwell time. This is the first model of its kind that can be used for studying area-crossing rates. To further emphasize the flexibility of the model, we have extended the model to study an overlapped location-area strategy. The study and analysis of overlapped locations areas has hitherto been difficult due to the complexity of the models.