The Robustness of Stochastic Switching Networks

Many natural systems, including chemical and biological systems, can be modeled using stochastic switching circuits. These circuits consist of stochastic switches, called pswitches, which operate with a fixed probability of being open or closed. The paper studies the effect caused by introducing an error of size ? to each pswitch in a stochastic circuit. The paper analyzes two constructions - simple series-parallel and general series-parallel circuits - and proves that simple series-parallel circuits are robust to small error perturbations, while general series-parallel circuits are not. Specifically, the total error introduced by perturbations of size less than ? is bounded by a constant multiple of ? in a simple series-parallel circuit, independent of the size of the circuit.