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Traditional approaches for capacity planning are based on queueing network models. However, modeling with queueing networks requires the knowledge of the service demands of each class of workloads at each device described in the model. In real systems, such service demands can be very difficult to measure. In this paper, we present an optimization-based technique to address the problem. The technique is formulated as a robust linear parameter estimation that can be used with both closed and open queueing network models. We consider the case where aggregate measurements (throughput and utilization) are available. Such measurements are typically much easier to obtain than the service demands. We present experimental results which prove the effectiveness of the constrained and robust linear estimation.