We consider the problem of embedding a discrete parameter queueing system into continuous space by using simulation-based interpolation. We first show that a discrete-time Geom/Geom/1 queue with service time T can be exactly simulated by making the service time a Bernoulli random variable which switches between T_1 and T_2 with T_1 < T < T_2 with expected value T. This is a form of simulation-based interpolation which can, in principle, be applied to more complex queueing networks. We show that such an interpolation is possible for  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. Unlike spatial interpolation, the interpolated value can be computed using a single simulation run irrespective of the number of parameters in the system. To demonstrate the utility of the interpolation scheme , we solve a discrete parameter queuing network optimization problem by embedding the discrete parameters into  continuous space, and then using a continuous space optimization algorithm to find optimal configurations .
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 .
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We consider the problem of embedding a discrete parameter queueing system into continuous space by using simulation-based interpolation. We first show that a discrete-time
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
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queue with service time T can be exactly simulated by making the service time a Bernoulli random variable which switches between T_1 and T_2 with T_1 < T < T_2 with expected value T. This is a form of simulation-based interpolation which can, in principle, be applied to more complex queueing networks. We
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
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interpolation
embedding
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more complex
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Unlike spatial interpolation, the interpolated value can be computed using a single simulation run irrespective of the number of parameters in the system.
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interpolation scheme
embedding technique
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discrete parameter
6-parameter
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a continuous space. The technique produces smooth interpolations of the objective function, and a
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space, and then using a continuous space optimization algorithm to find optimal configurations
optimizer applied directly over this embedding converges rapidly, producing good solutions