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Based on EAP-AKA for different wireless access networks, this paper mainly focuses on the optimal authentication scheme. First, an optimized interworking authentication architecture is proposed among 3GPP, WLAN and WiMAX. Additionally, we present an authentication analytic model for 3GPP-WiMAX, pointing out that the authentication signaling cost can not only be affected by the k value of the authentication vectors array at a time obtained by 3GPP AAA server from Home Subscriber Server (i.e. authentication center), but also be impacted by the times of re-authentication with the same AV. Finally, from the numerical simulations, it is desirable to provide guidelines for selecting an appropriate k, so as to achieve the best system performance.