Recently, several research groups have demonstrated that MVMs and linear systems can be performed analytically in a single time step with memristor crossbars. These two approaches can both be applied to Markov chains. We present circuit models for open-loop and feedback configurations, and perform analyses that include memristor programming errors, thermal noise sources and element nonidealities in realistic circuit simulations to determine both the precision and accuracy of the analog solutions. We provide mathematical tools to describe the trade-offs in the circuit model between power consumption and magnitude of errors. We compare the two approaches by analyzing Markov chains applications.