We consider large queueing networks for which transient and stationary probability distributions are very difficult or impossible to obtain due to the state space explosion. We apply the coupling by mapping functions in order to compare large size multidimensional Markov chains with smaller ones, generating bounds on stationary and transient performance measures. When the processes have many transitions due to several events, the coupling is not easy to apply. The goal of this work is to provide a general algorithm for the comparison using the coupling by mapping functions. This algorithm can be applied for the generation of aggregated bounding processes