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This paper presents two new methods that use local information alone to predict the resource demands of and determine resource reservation levels for future handoff calls in multimedia wireless IP networks. The proposed methods model the instantaneous resource demand directly. This differs from most existing methods that derive the demands from modeling the factors that impact the demands. As a result, the proposed methods allow new and handoff calls to: (1) follow non-Poisson and/or nonstationary arrival processes; (2) have arbitrary per-call resource demands; and (3) have arbitrarily distributed call and channel holding times. The first method is based on the Wiener prediction theory and the second method is based on time series analysis. Our simulations show that they perform well even for non-Poisson and nonstationary handoff call arrivals, arbitrary per-call bandwidth demands, and nonexponentially distributed call and channel holding times. They generate closely comparable performance with an existing local method and an existing collaborative method that uses information about mobiles in neighboring cells, under assumptions for which these other methods are optimized. The proposed methods are much simpler to implement than most other existing methods with fewer capabilities