Tail Quantile Estimation for Non-preemptive Priority Queues

TL;DR

This paper introduces an importance sampling-based regenerative simulation algorithm to efficiently estimate high quantiles of sojourn times in multi-class non-preemptive priority queues, addressing rare event sampling challenges.

Contribution

It develops a novel importance sampling method with a central limit theorem for quantile estimation in priority queueing systems, improving over existing benchmarks.

Findings

Algorithm outperforms benchmark methods in numerical experiments.

Provides a central limit theorem for the estimator.

Enhances rare event simulation in queueing systems.

Abstract

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.