Abstract. In characterizing statistical multiplexing models of network nodes important QoS measures are often to be estimated such as saturation probability and workload loss ratio. In the two main streams of multiplexer models (bufferless and buffered statistical multiplexers) the meaning of these measures and their possible estimations are different. In this paper, we set up a family of closed-form performance bounds which can be used for estimating QoS measures in both multiplexing models. The underlying approximation technique in the framewerk of bufferless fluid fiow multiplexing model (bffm) is systematically described, and besides the resultant new QoS measure estimates previously known ones arealso identified. The bounds in bffm have been analyzed and compared based on numerical investigations. The applicability of the performance bounds for buffered multiplexers is also briefiy discussed.