On Continuous-space Embedding of Discrete-parameter Queueing Systems

TL;DR

This paper introduces a novel randomization-based method to embed discrete queueing system parameters into continuous space, enabling efficient optimization using continuous methods even in high-dimensional settings.

Contribution

It presents a new embedding technique for discrete queue parameters into continuous space via randomization, suitable for high-dimensional optimization problems.

Findings

The embedding produces smooth objective function interpolations.

The method is computationally efficient regardless of parameter count.

Effective optimization demonstrated on a large queueing network case study.

Abstract

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.