The effect of compression and expansion on stochastic reaction networks

Markov chains are a fundamental model to study systemswith stochastic behavior. However, their state space is oftenof an unmanageable size, making the use of approximationsand simplifications necessary for analytic solutions. This thesisconsiders reaction networks as a well-known representationfor Markov chains describing interactions between speciespopulations. It presents several methods using model transformationsto aid with the effective analysis of such systems.Species equivalence is a reduction technique that lifts the concept(and related algorithms) of Markov chain lumpabilityfrom lumping of states to directly lumping species in a reactionnetwork. This allows the simplification of a reactionnetwork without first examining its state space.The tool DiffLQN implements a method for the analysis oflarge-scale stochastic models for the performance evaluationof software systems using an approach based on deterministicrate equations, by means of a compact system of ordinarydifferential equations that approximate only mean estimatesfor stochastic reaction networks.Deterministic rate equations are generally accurate for networkswith large populations, but may incur errors when elementsare only present in low copy numbers. This thesispresents finite state expansion, which aims to solve that problem.It does so by converting a given reaction network intoan expanded one with additional species and reactions suchthat the overall stochastic behavior is preserved. The resultingrate equations, however, may enjoy increased accuracy.Several tests on example models show that finite state expansionproves competitive with other state-of-the-art methods.