Rare-Event Simulation for Many-Server Queues

TL;DR

This paper introduces an asymptotically optimal rare-event simulation method for analyzing loss probabilities in large many-server queue systems, utilizing a measure-valued process framework to accurately capture system behavior during loss events.

Contribution

It presents the first asymptotically optimal rare-event simulation algorithm for many-server queues using a full measure-valued process descriptor.

Findings

Algorithm is proven to be asymptotically optimal.

Effective in estimating rare loss events in large systems.

Provides insights into system behavior during loss occurrences.

Abstract

We develop rare-event simulation methodology for the analysis of loss events in a many-server loss system under quality-driven regime, focusing on the steady-state loss probability (i.e. fraction of lost customers over arrivals) and the behavior of the whole system leading to loss events. The analysis of these events requires working with the full measure-valued process describing the system. This is the first algorithm that is shown to be asymptotically optimal, in the rare-event simulation context, under the setting of many-server queues involving a full measure-valued descriptor.