Before revision:  We first show that a discrete-time Geom/Geom/1 queue with service time T can be exactly simulated by making the service time a Bernoulli random variable which switches between T_1 and T_2 with T_1 < T < T_2 with expected value T. This is a form of simulation-based interpolation which can, in principle, be applied to more complex queueing networks. We show that such an interpolation is possible for  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:  We first show that a discrete-time 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 interpolation is possible for 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.