  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.
