Approximating closed fork-join queueing networks using product-form stochastic Petri-nets

Computing paradigms have shifted towards highly parallel processing and massive replication of data. This entails the efficient distribution of requests and the synchronization of results provided to users. Guaranteeing SLAs requires the ability to evaluate the performance of such systems while taking the effect of non-parallel workloads into consideration. This can be achieved with performance models that are able to represent both parallel and sequential workloads. This paper presents a product-form stochastic Petri-net approximation of fork-join queueing networks with interfering requests. We derive the necessary conditions that guarantee the accuracy of the approximations and verify this through examples in comparison to simulation. We apply these approximate models to the performance evaluation of replication in NoSQL cloud datastores and illustrate the composition of large models from smaller models, thus facilitating the ability to model a range of deployment scenarios. We show the efficiency of our solution method, which finds the product-form solution of the models without the representation of the state-space of the underlying CTMC.