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The future-generation wireless systems will combine heterogeneous wireless access technologies to provide mobile users with seamless access to a diverse set of applications and services. The heterogeneity in this inter-technology roaming paradigm magnifies the mobility impact on system performance and user perceived service quality, necessitating novel mobility modeling and analysis approaches for performance evaluation. In this paper, we present and compare three mobility models in two-tier integrated heterogeneous wireless systems, the independence model as a naive extension of the traditional cell residence time modeling techniques for homogeneous cellular networks, the basic Coxian model which takes into consideration the correlation between the residence time within different access technologies, and the extended-Coxian model for further improved estimation accuracy. We propose a general stochastic performance analysis framework based on application session models derived from these mobility models, applying it to a 3G-WLAN integrated system as an example. Our numerical and simulation results demonstrate the general superiority of Coxian-based mobility modeling over the independence model. Furthermore, using the proposed modeling and analysis methods, we investigate the impact of different parameters on system performance metrics such as network utilization time, handoff rates, and forced termination probability, for a wide range of user applications.