Before revision: We consider the problem of embedding a discrete parameter queueing system into continuous space by using simulation-based interpolation. 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.
After revision: In simulation-based optimization of queuing systems, the presence of discrete-valued parameters (such as buffer sizes and the number of servers) makes the optimization difficult. We propose a novel technique for embedding such discrete parameters into a continuous space, so that optimization can be performed efficiently using continuous-space methods. Unlike spatial interpolation, our embedding technique is based on a randomization of the simulation model. 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 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.