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In this paper, we address the question of dynamic net- work provisioning for time-varying traffic rates, with the objective of maximizing the system throughput. We assume that the network is capable of providing bandwidth guaranteed traffic tunnels for an ingress-egress pair and present an approach that (1) updates the tunnel routes and (2) adjusts the tunnel bandwidths, in an incremental, adaptive manner, based on the variations in the incoming traffic. First, we consider a simpler scenario where tunnel routes are fixed, and present an approach for adjusting the tunnel bandwidths dynamically. We show, through simulations, that our dynamic bandwidth assignment algorithm significantly outperforms the optimal static bandwidth provisioning policy, and yields a performance close to that of the optimal dynamic bandwidth provisioning policy. We also propose an adaptive route update algorithm, which can be used in conjunction with our dynamic bandwidth assignment policy, and leads to further improvement in the overall system performance.