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In guaranteed Quality of Service (QoS) packet networks like future QoS Internet quantifying resource usage is a key issue for traffic management. Within this the estimated bandwidth requirements of traffic flows are apparently important building blocks of decisions made by connection admission control, QoS routing and resource reservation protocols. This paper focuses on bandwidth requirement estimators under the framework of bufferless fluid flow multiplexing (bffm) which is a suitable modeling approach for scenarios with high network utilization with large number of traffic flows multiplexed. The bandwidth requirement estimates proposed have acceptable accuracy and are parsimonious, that is they need very few pieces of information on traffic flows which are either measurable in straightforward manner or known a priori and propagated through the nodes of networks. These properties are essential for efficient implementations.