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 service (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 and compare both methods. Large Deviations Theory applications to Data Networks are mainly based on the many sources asymptotic. This asymptotic is adequate for networks like Internet 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 model called many sources and small buffer asymptotic. They give a formula to calculate the link overflow probability and the end-to-end Loss Ratio of traffic streams in a virtual path feed forward network of general topology. They also define the fictitious network concept. The fictitious network has the same topology than the real one, but each traffic stream goes across a link on its path without being affected by the upstream links until that one. So, in the fictitious network each internal link can be analysed as an external one. Therefore, the fictitious network usage simplifies dramatically the network performance analysis. Our main motivation to simplify this task is to allow on-line performance analysis and traffic engineering 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-utilization. Undercertain conditions the real and the fictitious network analysis give the same results (there is no overestimation). In this work we establish sufficient conditions 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 and fictitious networks analysis give different results, we find a method to bound the overestimation. Finally, we show some numerical examples to compare the performance analysis in the real vs. the fictitious network, and to validate our main results.