Simterpolation: A simulation based interpolation approximation for queueing systems

In this paper, the authors approximate moments of the sojourn time distribution in open networks of priority queues via an interpolation approximation. The interpolation is constructed from five random variables (and their covariance matrix) that are simultaneously estimated from a single regenerative simulation of the system at any arrival rate. The random variables are consistent estimates of the zeroth and first-order light traffic limits, the heavy traffic limit, and the value of the function and its derivative at the arrival rate of the simulation. The data yield a least squares estimate of a normalized version of the original function, which, in turn, yields an estimate of the function of interest. This procedure is useful for complex systems because the light and heavy traffic limits needed for an interpolation are not easy to calculate analytically in those cases.