  We develop a robust queueing network analyzer algorithm to approximate the
steady-state performance of a single-class open queueing network of
single-server queues with Markovian routing. The algorithm allows non-renewal
external arrival processes, general service-time distributions and customer
feedback. We focus on the customer flows, defined as the continuous-time
processes counting customers flowing into or out of the network, or flowing
from one queue to another. Each flow is partially characterized by its rate and
a continuous function that measures the stochastic variability over time. This
function is a scaled version of the variance-time curve, called the index of
dispersion for counts (IDC). The required IDC functions for the flows can be
calculated from the model primitives, estimated from data or approximated by
solving a set of linear equations. A robust queueing technique is used to
generate approximations of the mean steady-state performance at each queue from
the IDC of the total arrival flow and the service specification at that queue.
The algorithm effectiveness is supported by extensive simulation studies and
heavy-traffic limits.
