Automatic construction of product-form solutions in stochastic networks

The growing complexity of modern systems has escalated the need for performance metrics. Stochastic models such as queuing networks and stochastic Petri nets have been used to model these systems so that their performance measures can be evaluated analytically. Product-form solutions are equilibrium state probabilities in networks of stochastic nodes (e.g. queues) in the form of a product of terms relating to each node separately. One can derive various performance metrics from these product form solutions, thus there is considerable effort dedicated to finding them in various stochastic models. An established theorem, the Reversed Compound Agent Theorem (RCAT), derives mechanically the product-form solutions for stochastic models defined as a composition of two or more smaller stochastic models, under some conditions. Its use of the divide-and-conquer approach solves problems of state space explosion and computational complexity, which standard methods face while finding product-forms for large and complex networks. This report presents a working implementation of RCAT in MATLAB and its extension Multiple Agent RCAT which can be applied to a wide variety of queuing networks with multiple components. It also provides the first working implementation of RCAT applied to stochastic Petri nets thus expanding its utility to analyse models composed of both Petri nets and queuing networks.