This paper presents a method of comparing two queueing networks. In this context one typically thinks of one network as being a solvable modification of another unsolvable one of practical interest. The approach is essentially based upon evaluating steady-state performance measures by a cumulative reward structure and strongly relies upon the analytical estimation of so-called bias terms. To this end, in contrast with the standard stochastic comparison approach, a Markov reward approach is presented. This approach is based upon a discrete-time transformation and one-step Markov reward or dynamic programming steps. The essential ingredients of this approach, in more detail, are - to analyze steady-state performance measures via expected average rewards; - to use a discrete-time Markov transition structure and to compare the difference of the two systems in its one-step transition structure; - to use inductive arguments to estimate or bound the so-called bias terms for one of the two systems. Leonardo Pasini