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Simterpolations: estimating an entire queueing function from a single sample path

We present an overview of a method for estimating an entire queueing function, ƒ(λ), 0 ≤ λ < c, from a single simulation sample path, where λ is the arrival rate to the system and c is the system capacity. For example, ƒ(λ) could be the average sojourn time in a queueing network as a function of λ. Recently methods have been developed that allow one to simultaneously estimate ƒ(0), ƒ'(0), ƒ(λ*) ƒ'(λ*), and h (the heavy traffic limit of ƒ) based on the sample path from a single simulation experiment in which the arrival rate to the system is λ*. 'Standard' simulation methodology has generally focused on obtaining only the point estimate of ƒ(λ*) from this one sample path. The computational costs associated with obtaining all five estimates (as well as an estimate of the asymptotic covariance of the estimates) is only slightly higher than the costs associated with obtaining an estimate of ƒ (λ*) alone. We propose a regenerative simulation methodology to construct estimates of ƒ(0), ƒ'(0), ƒ(λ*) ƒ'(λ*), and h and an approximation to the joint distribution of the estimates. We then outline a method for fitting a polynomial to a 'normalized' version of the estimates. A reverse normalization of the fitted polynomial yields an estimate of ƒ(λ), 0 ≤ λ < c.