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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 nonrenewal external arrival processes, general service‐time distributions and customer feedback. The algorithm is based on a decomposition approximation, where 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 external arrival processes can be calculated from the model primitives or estimated from data. Approximations for the IDC functions of the internal flows are calculated by solving a set of linear equations. The theoretical basis is provided by heavy‐traffic limits for the flows established in our previous papers. 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's effectiveness is supported by extensive simulation studies.