When provisioning the quantitative QoS based VPN services over packet switched networks, parameters such as packet loss, delay and delay jitter, besides the required bandwidth, have to be guaranteed. While the bandwidth is easier to guarantee during the lifetime of a VPN service, maintaining a value of the loss parameter below a preset value presents serious difficulties. Thus one of the main issues to be solved is to estimate the packet loss parameter effectively and accurately. Linking the stochastic characteristics of the traffic process to the loss probability has been examined as a solution under various contexts. Based on the large deviation theory (LDT), two types of asymptotic loss estimators have been studied extensively: the large buffer asymptotic and the large number of source asymptotic. This paper explores the application of the above estimators to the core links which aggregates lots of VPN services. To reduce the computational complexity, aggregate traffic approximation estimator is employed instead on the latter of the study. Firstly, the two practical estimators are derived based on LDT and Gaussian traffic model. Then their performances are evaluated in the live MPLS VPN network. Conclusion and suggestion for future research are formulated at the end of this paper.