  Motivated by applications in computing and telecommunication systems, we
investigate the problem of estimating p-quantile of steady-state sojourn times
in a single-server multi-class queueing system with non-preemptive priorities
for p close to 1. The main challenge in this problem lies in efficient sampling
from the tail event. To address this issue, we develop a regenerative
simulation algorithm with importance sampling. In addition, we establish a
central limit theorem for the estimator to construct the confidence interval.
Numerical experiments show that our algorithm outperforms benchmark simulation
methods. Our result contributes to the literature on rare event simulation for
queueing systems.
