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There are many efforts to adapt streaming services to wireless mobile networks. It is hard to assure the QoS of the streaming services in wireless mobile networks because a terminal moves continuously and causes handoff procedures. We focus on delay factors which occur whenever a terminal moves in the wireless mobile environment. It is assumed that a mobile terminal's movement is based on the Gauss-Markov model with the varying velocity affected by its previous velocity. Using this model, we can predict the mobility pattern of a moving terminal and the delay of streaming services caused from handoff procedures during its moving. To compensate the streaming service delay, the paper proposes a dynamic rate control scheme for streaming services based on the next-handoff prediction using the Gauss-Markov model, which is the predictive mobility model based on the varying velocity and the handoff occurrence rates according to the time.