An approach is provided for auto-bandwidth adjusting bandwidth allocations for traffic-engineered tunnels used to carry traffic along a network. Traffic over the tunnel is sampled at a first interval period and at a second interval period, where the second interval period is shorter than the first interval period. A determination is made as to whether the sampled traffic taken using the second interval period is greater than the bandwidth allocation, and the bandwidth allocation is adjusted upward based upon a determination that the sampled traffic taken using the second interval period is greater than the bandwidth allocation. Also, a determination can be made as to whether the sampled traffic taken using the first interval period is less than the bandwidth allocation, and the bandwidth allocation can be adjusted downward based upon a determination that the sampled traffic taken using the first interval period is less than the bandwidth allocation.