Accurate measurement of queue distributions is vital to guarantee the QoS performance in packet networks, e.g. IP. Measurement is particularly difficult when the packet traffic is governed by extremely high variance power laws. A measurement scheme is proposed to estimate the queue length distribution for aggregate power law on-off sources multiplexed into a FIFO queue. This scheme is carried out on a non-intrusive basis, so in contrast to active measurement methods, it will not create extra traffic. The methodology is validated with simulation, and results show excellent agreement between estimated and actual queue length distribution, even in the presence of traffic with extremely high variance. This can therefore be used as the core mathematical part of a packet network-based assurance technique.