Light traffic derivatives via likelihood ratios.

We consider the steady-state behavior of open queueing systems with Poisson arrival processes in light traffic, that is, as the arrival rate tends to zero. We provide expressions for derivatives of various quantities of interest (such as moments of steady state sojourn times and queue lengths) with respect to the arrival rate, at an arrival rate of zero. These expressions are obtained using the regenerative structure of the queueing system, along with a change of measure formula based on likelihood ratios. The derivatives, which can be used in interpolation approximations, may be evaluated analytically in simple cases, and by simulation in general.