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 queues. We prove that the randomization produces valid interpolations of the steady-state performance functions with respect to an integer service-time parameter. We then show that such an embedding is possible for more complex queueing networks whose parameters can include deterministic service times, queue capacities, and the number of servers , and empirically demonstrate that the interpolation is well behaved. To demonstrate the utility of the embedding technique, we solve a 6-parameter queuing network optimization problem by embedding the discrete parameters into a continuous space . The technique produces smooth interpolations of the objective function , and a continuous optimizer applied directly over this embedding converges rapidly, producing good solutions.
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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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
Motivated by the problem of discrete-parameter simulation optimization (DPSO) of queueing systems, we consider the problem of embedding the discrete parameter space
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space, so that optimization can be performed efficiently using
one so that descent-based
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. Unlike spatial interpolation, our embedding technique is based on
could be directly applied for efficient optimization. We show that
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. The interpolated value can be computed using a single simulation of this randomized model, irrespective
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
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. We first study the theoretical properties of such a randomization scheme applied to M/M/1 and Geom/Geom/1 queues. We prove that the randomization produces valid interpolations of the steady-state performance functions with respect to an integer service-time parameter. We then show that such an embedding is possible for more complex queueing networks whose parameters can include deterministic service times,
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
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and the
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, and empirically demonstrate that the interpolation is well behaved. To demonstrate the utility of the embedding technique, we solve a 6-parameter queuing network optimization problem by embedding the discrete parameters into a continuous space . The technique produces
and server-delay parameters into continuous space and empirically show that the technique can produce
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, and a continuous optimizer applied directly over this embedding converges rapidly, producing
. 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