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 problem. In performance analysis, we need in general to study only a part of the network (a node or a path). Thus, we propose to define bounding systems that lead to compute bounds on performance measures of the considered subsystem. The original large state space is mapped into a smaller space to overcome the state space explosion problem, and bounds both on stationary and on transient performance measures are computed from these reduced-size models. This approach provides an interesting solution for complex networks since we have a trade-off between the quality of the bounds and the state space size, thus the computational complexity. As an application, we study a general multi-server queueing network, with finite capacity queues. We define bounding systems to compute blocking probabilities. The influence of parameters on the precision of the computed bounds are studied through some numerical examples in order to give more insights into the proposed approach.