End to end QoS (Quality of Service) is crucial in computer networks, but very hard to study as the systems are in general very complex. We suppose that systems can be modeled by multidimensional Markov processes, which could be very hard to analyse if there is no specific solution form. We propose to apply stochastic comparisons of Markov processes in order to solve this problem. We provide new processes, easier to analyze and representing stochastic bounds (upper or lower) for the original model. In this paper, we propose strong and weak bounding processes for a general queueing network model, and discuss their accuracy for QoS constraints