The performance analysis of a link is a well studied problem. However, for a service provider the most interesting issue is the end-to-end quality of serv ice (QoS) evaluation. The focus of this work is to go from the link to the network analysis. This can be done in a complete but complex way or using an approximation to speedup the calculations. We analyse an d compare both methods. Large Deviations Theory applications to Data Networks are m ainly based on the many sources as- ymptotic. This asymptotic is adequate for networks like Int ernet backbones, where the assumption that the network is fed by a large number of sources is reasonable. Recently, Ozturk et al. have proposed a slightly different mo del called many sources and small buffer asymptotic. They give a formula to calculate the link overflo w probability and the end-to-end Loss Ratio of traffic streams in a virtual path feed forward network of gen eral topology. They also define the fictitious network concept. The fictitious network has the same topology than th e real one, but each traffic stream goes across a link on its path without being affected by the ups tream links until that one. So, in the fictitious network each internal link can be analysed as an ex ternal one. Therefore, the fictitious network usage simplifies dramatically the network performance anal ysis. Our main motivation to simplify this task is to allow on-line performance analysis and traffic engi- neering algorithms in virtual path networks as MPLS or ATM. Ozturk et al. show that the fictitious network overestimates the overflow probability and the end to end Loss Ratio. Therefore, decisions based on the fictitious network analysis are safe. However, this overestimation leads to network resources under-utilizat ion. Under certain conditions the real and the fictitious network analysis give the same results (there is no overestimation). In this work we establish sufficient cond itions to assure that this coincidence arises. Those conditions are not necessary, and we give an easy way to check if exact results may be obtained even though sufficient conditions are not met. When the real an d fictitious networks analysis give different results, we find a method to bound the overestimation. Finally, we show some numerical examples to compare the perf ormance analysis in the real vs. the fictitious network, and to validate our main results