Dynamic importance sampling for queueing networks

TL;DR

This paper introduces a novel dynamic importance sampling method tailored for queueing networks, addressing limitations of traditional fixed-measure approaches by leveraging differential games and Isaacs equations to efficiently estimate rare event probabilities.

Contribution

It develops and analyzes a new dynamic importance sampling scheme for queueing networks, improving efficiency over fixed-measure methods by incorporating differential game insights.

Findings

Effective importance sampling schemes for tandem Jackson networks.

Successful application to networks with feedback and large backlog events.

Demonstrated improved simulation efficiency for rare queue overflow events.

Abstract

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The standard approach, which simulates the system using an a priori fixed change of measure suggested by large deviation analysis, has been shown to fail in even the simplest network setting (e.g., a two-node tandem network). Exploiting connections between importance sampling, differential games, and classical subsolutions of the corresponding Isaacs equation, we show how to design and analyze simple and efficient dynamic importance sampling schemes for general classes of networks. The models used to illustrate the approach include $d$-node tandem Jackson networks and a two-node network with feedback, and the rare events studied are those of large queueing backlogs, including total population overflow and the overflow of individual buffers.