The provisioning of QoS in the Internet is gaining an increasing attention, thus the importance of methods capable of estimating the bandwidth requirement of traffic flows is constantly growing. This information can be used for a wide range of purposes. Admission control, QoS routing and load sharing all need the same basic information in order to be able to make decisions. This paper describes a number of methods that can be used to arrive at precise estimates of the bandwidth requirement focusing on those that are based on the theory of large deviations. A methodology is presented that allows the reformulation of earlier solutions based on the estimation of some form of an overflow probability so that their output becomes a bandwidth-type quantity, the format preferred by Internet control applications. The methodology provides two tracks for the conversion: an indirect method that encapsulates the overflow probability-type approach as an embedded calculation and a direct method that immediately results in the estimate of the bandwidth requirement. The paper introduces a novel method for the direct computation of the bandwidth requirement of Internet traffic flows using the many sources asymptotic regime of the large deviation theory. The direct bandwidth estimator method reduces the computational complexity of the calculations, since it results directly in the bandwidth requirement, allowing the omission of the frequent and costly computation of the buffer overflow probability. The savings arising from the reduction in computational complexity are demonstrated in a numerical example.