  Traffic flow count data in networks arise in many applications, such as
automobile or aviation transportation, certain directed social network
contexts, and Internet studies. Using an example of Internet browser traffic
flow through site-segments of an international news website, we present
Bayesian analyses of two linked classes of models which, in tandem, allow fast,
scalable and interpretable Bayesian inference. We first develop flexible
state-space models for streaming count data, able to adaptively characterize
and quantify network dynamics efficiently in real-time. We then use these
models as emulators of more structured, time-varying gravity models that allow
formal dissection of network dynamics. This yields interpretable inferences on
traffic flow characteristics, and on dynamics in interactions among network
nodes. Bayesian monitoring theory defines a strategy for sequential model
assessment and adaptation in cases when network flow data deviates from
model-based predictions. Exploratory and sequential monitoring analyses of
evolving traffic on a network of web site-segments in e-commerce demonstrate
the utility of this coupled Bayesian emulation approach to analysis of
streaming network count data.
