The effect of compression and expansion on stochastic reaction networks

Markov chains are a fundamental model to study systems with stochastic behavior. However, their state space is often of an unmanageable size, making the use of approximations and simplifications necessary for analytic solutions. This thesis considers reaction networks as a well-known representation for Markov chains describing interactions between species populations. It presents several methods using model transformations to aid with the effective analysis of such systems. Species equivalence is a reduction technique that lifts the concept (and related algorithms) of Markov chain lumpability from lumping of states to directly lumping species in a reaction network. This allows the simplification of a reaction network without first examining its state space. The tool DiffLQN implements a method for the analysis of large-scale stochastic models for the performance evaluation of software systems using an approach based on deterministic rate equations, by means of a compact system of ordinary differential equations that approximate only mean estimates for stochastic reaction networks. Deterministic rate equations are generally accurate for networks with large populations, but may incur errors when elements are only present in low copy numbers. This thesis presents finite state expansion, which aims to solve that problem. It does so by converting a given reaction network into an expanded one with additional species and reactions such that the overall stochastic behavior is preserved. The resulting rate equations, however, may enjoy increased accuracy. Several tests on example models show that finite state expansion proves competitive with other state-of-the-art methods.