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QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks

The Quadratic Reduction Framework (QRF) is a numerical modeling framework to evaluate complex stochastic networks composed of resources featuring queueing, blocking, state-dependent behavior, service variability, temporal dependence, or a subset thereof. Systems of this kind are abstracted as network of queues for which QRF supports two common blocking mechanisms: blocking-after-service and repetitive-service random-destination. State-dependence is supported for both routing probabilities and service processes. To evaluate these models, we develop a novel mapping, called Blocking-Aware Quadratic Reduction (BQR), which can describe an intractably large Markov process by a large set of linear inequalities. Each model is then analyzed for bounds or approximate values of performance metrics using optimization programs that provide different levels of accuracy and error guarantees. Numerical results demonstrate that QRF offers very good accuracy and much greater scalability than exact analysis methods.