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The rapid development and deployment of integrated heterogeneous networking environments such as third generation (3G) cellular WANs and WLANs will soon become commonplace. Users will demand connectivity without disruption anywhere and anytime. Mobility implies that this can only be done using either horizontal or vertical handover techniques where connections will be seamlessly switched between available networks. However, handover policies must consider issues such as network coverage, mobility, as well as Quality of Service (QoS). Analytical models are therefore required to deal with this complexity. However, there have been no analytical models that could be used as part of an overall framework. This paper addresses these issues by developing an analytical model to study vertical handover between a WLAN and a cellular system such as 3G. This model includes mobility of the users as well as decision making probabilities about handover between the two networks. In this paper the cellular network is modelled as a multi-channel queuing system while the WLAN is depicted as a single channel queuing system, both with finite buffering limits. The exact spectral expansion method is employed to solve this model. The proposed analytical model and its solution can be used to evaluate the QoS measures of such systems efficiently and accurately. Numerical results for mean queue length and blocking probability are computed and presented for both systems.