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arXiv · 1606.02900

On Continuous-space Embedding of Discrete-parameter Queueing Systems

Neha Karanjkar·Madhav P. Desai·Shalabh Bhatnagar
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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.

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Neha Karanjkar, Madhav P. Desai, Shalabh Bhatnagar. 2016-06-09. On Continuous-space Embedding of Discrete-parameter Queueing Systems. https://arxiv.org/abs/1606.02900

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