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The GI/G/1 queueing model is regarded as a functional which maps the service and interarrival time distributions onto output quantities of interest, such as the stationary waiting time distribution. For the case where the input distributions have densities, techniques from infinite-dimensional analysis are used to obtain derivatives and Taylor series expansions for the functionals. These yield approximations to the output distributions which can be viewed as nonparametric alternatives to parametric approximations such as those provided by infinitesimal perturbation analysis or the phase method

A Functional Approach to the Stationary Waiting Time and Idle Period Distributions of the GI/G/1 Queue