Light traffic derivatives via likelihood ratios

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