  A graph-theoretic analysis of the steady-state behavior of an open Jackson
queueing network is developed. In particular, a number of queueing-network
performance metrics are shown to exhibit a spatial dependence on local drivers
(e.g. increments to local exogenous arrival rates), wherein the impacts fall
off across graph cutsets away from a target queue. This graph-theoretic
analysis is also used to motivate a structure-preserving model reduction
algorithm, and an algorithm that exactly matches performance statistics of the
original model is proposed. The graph-theoretic results and model-reduction
method are evaluated via simulations of an example queueing-network model.
