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In this paper, we propose a universal mobile telecommunications system (UMTS) and a wireless LAN (WLAN) interworking solution called WLAN-based general packet radio service (GPRS) support node (WGSN), which allows a UMTS/WLAN dual mode mobile station (MS) to access heterogeneous wireless services. To reduce the power consumption of an MS, most WGSN applications are not activated at the MS, and MS-terminated services, such as incoming voice over IP (VoIP) calls, are not supported. To address this issue, a push mechanism called session initiation protocol (SIP)-based push center (SPC) was implemented in the WGSN node. For an incoming call to an MS, the SPC utilizes the UMTS short message service to activate the SIP User Agent of the MS. We study the performance of the SPC. An analytic model is proposed to derive the expected number of lost calls during the activation period. The analytic results are validated against the simulation experiments. Our study quantitatively indicates how the SPC performance is affected by the activation time and the timeout period, and we also suggest how to select appropriate values of these two factors to optimize the SPC performance.