On Continuous-space Embedding of Discrete-parameter Queueing Systems
  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. 
Neha Karanjkar and Madhav P. Desai and Shalabh Bhatnagar
cs.PF math.OC