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The main feature of the next generation wireless communication systems is the ability to establish ubiquitous and seamless access to various radio access technologies (RATs) and standards. For this reason the integration of cellular and wireless local area networks (WLANs) and performance evaluation of the interaction between these technologies is now an important research area. Modelling such systems for performance evaluation is essential to improve the architecture according to the quality of service (QoS) requirements and performance characteristics. In this paper, an analytical model for performance evaluation of an integrated cellular network and a WLAN is considered. WLAN is deployed inside of the cellular network to support handoffs between cellular networks with higher bandwidth. Such an integrated system can be modelled as a two stage open network. An analytical model is proposed together with an exact solution technique in order to evaluate the performance of an integrated system consisting of a cellular network and a WLAN. A two stage queuing system is considered for this purpose. Numerical results are presented for mean queue length values of cellular system as well as the WLAN.