  The substantial growth of network traffic speed and volume presents practical
challenges to network data analysis. Packet thinning and flow aggregation
protocols such as NetFlow reduce the size of datasets by providing structured
data summaries, but conversely this impedes statistical inference. Methods
which aim to model patterns of traffic propagation typically do not account for
the packet thinning and summarisation process into the analysis, and are often
simplistic, e.g.~method-of-moments. As a result, they can be of limited
practical use.
  We introduce a likelihood-based analysis which fully incorporates packet
thinning and NetFlow summarisation into the analysis. As a result, inferences
can be made for models on the level of individual packets while only observing
thinned flow summary information. We establish consistency of the resulting
maximum likelihood estimator, derive bounds on the volume of traffic which
should be observed to achieve required levels of estimator accuracy, and
identify an ideal family of models. The robust performance of the estimator is
examined through simulated analyses and an application on a publicly available
trace dataset containing over 36m packets over a 1 minute period.
