Before revision:  The interpolated value can be computed using a single simulation of this randomized model, irrespective of the number of parameters . We first study the theoretical properties of such a randomization scheme applied to M/M/1 and Geom/Geom/1 queues. We prove that the randomization produces valid interpolations of the steady-state performance functions with respect to an integer service-time parameter. We then show that such an embedding is possible for more complex queueing networks whose parameters can include deterministic service times, queue capacities, and the number of servers , and empirically demonstrate that the interpolation is well behaved.
After revision:  The interpolated value can be computed using a single simulation of this randomized model, irrespective of the number of parameters in the system, making the approach ideally suited to high-dimensional problems. We describe in detail the application of this technique to discrete-time queues for embedding queue capacities, and the number of servers , and empirically demonstrate that the interpolation is well behaved.