  Motivated by the problem of discrete-parameter simulation optimization (DPSO)
of queueing systems, we consider the problem of embedding the discrete
parameter space into a continuous one so that descent-based continuous-space
methods could be directly applied for efficient optimization. We show that a
randomization of the simulation model itself can be used to achieve such an
embedding when the objective function is a long-run average measure. Unlike
spatial interpolation, the computational cost of this embedding is independent
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, number of
servers and server-delay parameters into continuous space and empirically show
that the technique can produce smooth interpolations of the objective function.
Through an optimization case-study of a queueing network with $10^7$ design
points, we demonstrate that existing continuous optimizers can be effectively
applied over such an embedding to find good solutions.
