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In the Universal Mobile Telecommunication System (UMTS), authentication functions are utilized to identify and authenticate a mobile station (MS) and validate the service request type to ensure that the user is authorized to use the particular network services. The authenticating parties are the authentication center (AuC) in the home network and the MS. In the UMTS, the serving general packet radio service support node (SGSN) accesses the AuC to obtain the authentication data, and delegates the AuC to perform mutual authentication with the MS. Since the cost for accessing AuC is expensive, the SGSN may obtain an array of authentication vectors (AVs) at a time so that the number of accesses can be reduced. On the other hand, if the size K of the AV array is large, the AV array transmission from the AuC to the SGSN may be expensive. Thus, it is desirable to select an appropriate K value to minimize the authentication network signaling cost. We propose an analytic model to investigate the impact of K on the network signaling traffic, which is validated by simulation experiments. Then, we propose an automatic K-selection mechanism that dynamically selects the size of the AV array to reduce the network signaling cost. Our study indicates that the automatic K-selection mechanism effectively identifies appropriate size of the authentication vector array.