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Packet-level measurement is now critical to many aspects of broadband networking, for example for guaranteeing service level agreements, facilitating measurement-based admission control algorithms and performing network tomography. Because it is often impossible to measure all the data passing across a network, the most widely used method of measurement works by injecting probe packets. The probes provide samples of the packet loss and delay, and from these samples the loss and delay performance of the traffic as a whole can be deduced. However, measuring performance like this is prone to errors. Recent work has shown that some of these errors are minimised by using a gamma renewal process as the optimal pattern for the time instants at which to inject probes. This leaves the best rate at which to inject probes as the key unsolved problem, and this is addressed here by using the statistical principles of the design of experiments. The experimental design approach allows one to treat packet-level measurements as numerical experiments that can be designed optimally. Modelling the overflow of buffers as a 2-state Markov chain, the system's likelihood function is deduced, and from this a technique (using the Fisher information matrix) to determine the upper-bound on the optimal rate of probing is developed. A generalisation of this method accounts for the effect of the probed observations interfering with the experiment. The numerical results focus on VoIP traffic, allowing one to show how this methodology would be used in practice. One application of this is in measurement-based admission control algorithms, where the technique can be used to provide an upper-bound on the rate at which probes should be injected to monitor the loss performance of the target network, prior to making an admit/do not admit decision.