Approximating Fork-Join Systems via Mixed Model Transformations

While product-form queueing networks are effective in analyzing system performance, they encounter difficulties in scenarios involving internal concurrency. Moreover, the complexity introduced by synchronization delays challenges the accuracy of analytic methods. This paper proposes a novel approximation technique for closed fork-join systems, called MMT, which relies on transformation into a mixed queueing network model for computational analysis. The approach substitutes fork and join with a probabilistic router and a delay station, introducing auxiliary open job classes to capture the influence of parallel computation and synchronization delay on the performance of original job classes. Evaluation experiments show the higher accuracy of the proposed method in forecasting performance metrics compared to a classic method, the Heidelberger-Trivedi transformation. This suggests that our method could serve as a promising alternative in evaluating queueing networks that contains fork-join systems.