It is widely expected that next-generation wireless communication systems will be heterogeneous, integrating a wide variety of wireless access networks. Of particular interest recently is a mix of cellular networks (GSM/GPRS and WCDMA) and wireless local area networks (WLANs) to provide complementary features in terms of coverage, capacity and mobility support. If cellular/ WLAN interworking is to be the basis for a heterogeneous network then the analysis of complex handover traffic rates in the system (especially vertical handover) is one of the most essential issues to be considered. This thesis describes the application of queueing-network theory to the modelling of this heterogeneous wireless overlay system. A network of queues (or queueing network) is a powerful mathematical tool in the performance evaluation of many large-scale engineering systems. It has been used in the modelling of hierarchically structured cellular wireless networks with much success, including queueing network modelling in the study of cellular/ WLAN interworking systems. In the process of queueing network modelling, obtaining the network topology of a system is usually the first step in the construction of a good model, but this topology analysis has never before been used in the handover traffic study in heterogeneous overlay wireless networks. In this thesis, a new topology scheme to facilitate the analysis of handover traffic is proposed. The structural similarity between hierarchical cellular structure and heterogeneous wireless overlay networks is also compared. By replacing the microcells with WLANs in a hierarchical structure, the interworking system is modelled as an open network of Erlang loss systems and with the new topology, the performance measures of blocking probabilities and dropping probabilities can be determined. Both homogeneous and non-homogeneous traffic have been considered, circuit switched and packet-switched. Example scenarios have been used to validate the models, the numerical results showing clear agreement with the known validation scenarios.