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Secure group communication has become an important network issue as more emerging network applications now are based on a group communication model In a dynamic network, a group membership can be changed dynamically. That is, new members can join and current members can leave at any time. Instead of individual rekeying, i.e., performing a rekey right after each join or leave request is received, periodic batch rekeying has been proposed to alleviate rekeying overhead in resource-constrained wireless networks. The issue of how often rekey operations should be performed, however, has not been addressed. In this paper, we develop a stochastic Petri net (SPN) model to identify the optimal batch rekey interval to minimize periodic rekey overhead while satisfying application-specific constraints in rekey delay and secrecy violation. We develop three new threshold-based schemes, demonstrate the optimal rekey intervals for these three schemes, and identify the best scheme that should be adopted for periodic batch rekeying to minimize rekey overhead, when given a set of parameter values characterizing the operational and environmental conditions.