SMVA: A Stable Mean Value Analysis Algorithm for Closed Systems with Load-Dependent Queues

The load-dependent Mean Value Analysis (MVA) algorithm suffers from numerical instability issues. Different techniques have been adopted to avoid these issues, however, they have either complexity problems or restrictive assumptions. In this paper, we introduce a numerically Stable MVA (SMVA) algorithm for closed product-form queueing networks that allows for load-dependent queues. The SMVA algorithm is inspired by Seidmann’s approximation for the numerical stability, and employs the Bard-Schweitzer approximation for the accuracy. The SMVA algorithm offers a numerically stable, efficient, and accurate approximate solution. We validate SMVA by comparing it to other MVA algorithms in concrete examples, and analyse its errors. We also extend it to a multi-class model.