Current mobile users are often equipped with several network interfaces, which may be of different access technologies. Each access technology has specific characteristics in terms of coverage area and technical characteristics (band-width, QoS, etc.) and provides diverse commercial opportunities for the operators. It seems likely that these various technologies have to coexist and, from then, solutions of integration and interoperability will be necessary to deal with the technological diversity. We consider in this paper the WiMAX and ad-hoc integrated networks. A user who needs to establish a high reliable service prefers to use WiMAX network and another who needs to transmit Best Effort traffic with high rate but delay tolerant prefers to connect ad-hoc network that is assumed to have access to Internet. We aim through this combination to locally extend the coverage of WiMAX cell and to study the stability of involved nodes, in particular, gateway nodes. Under stability condition , our main result is characterization of the end-to-end throughput and delay using the rate balance equation and a G/G/1 queueing model. Through numerical results, we demonstrate the utility and efficiency of our approach.