In this work, we consider an approximation of the so-called far-end-tail distribution of processes describing quality of service (QoS) performance of queueing systems. This approximation is based on the asymptotic equivalence between the excess distribution over a high threshold and the generalized Pareto distribution, for a wide class of the governing distributions. The numerical results based on the regenerative estimation of a large deviation of the maximal workload over the regeneration cycle, in the queueing system M/G/1 with Pareto service time, are also presented, which verify theoretical results.