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Performance Evaluation and Policy Selection in Multiclass Networks
, 2002
"... This paper concerns modelling and policy synthesis for regulation of multiclass queueing networks. A 2parameter network model is introduced to allow independent modelling of variability and mean processingrates, while maintaining simplicity of the model. Policy synthesis is based on consideration ..."
Abstract

Cited by 46 (26 self)
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This paper concerns modelling and policy synthesis for regulation of multiclass queueing networks. A 2parameter network model is introduced to allow independent modelling of variability and mean processingrates, while maintaining simplicity of the model. Policy synthesis is based on consideration of more tractable workload models, and then translating a policy from this abstraction to the discrete network of interest. Translation is made possible through the use of safetystocks that maintain feasibility of workload trajectories. This is a wellknown approach in the queueing theory literature, and may be viewed as a generic approach to avoid deadlock in a discreteevent dynamical system. Simulation is used to evaluate a given policy, and to tune safetystock levels. These simulations are accelerated through a variance reduction technique that incorporates stochastic approximation to tune the variance reduction. The search for appropriate safetystock levels is coordinated through a cutting plane algorithm. Both the policy synthesis and the simulation acceleration rely heavily on the development of approximations to the value function through fluid model considerations.
Adaptive control variates for finitehorizon simulation
 Math. Oper. Res
, 2007
"... Adaptive Monte Carlo methods are simulation efficiency improvement techniques designed to adaptively tune simulation estimators. Most of the work on adaptive Monte Carlo methods has been devoted to adaptively tuning importance sampling schemes. We instead focus on adaptive methods based on control ..."
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Cited by 10 (2 self)
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Adaptive Monte Carlo methods are simulation efficiency improvement techniques designed to adaptively tune simulation estimators. Most of the work on adaptive Monte Carlo methods has been devoted to adaptively tuning importance sampling schemes. We instead focus on adaptive methods based on control variate schemes. We introduce two adaptive control variate methods, and develop their asymptotic properties. The first method uses stochastic approximation to adaptively tune control variate estimators. It is easy to implement, but it requires some nontrivial tuning of parameters. The second method is based on sample average approximation. Tuning is no longer required, but it can be computationally expensive. Numerical results for the pricing of barrier options are presented to demonstrate the methods. 1
Variance reduction for simulation in multiclass queueing networks
 IIE Transactions on Operations Engineering
, 1999
"... We use simulation to estimate the steadystate performance of a stable multiclass queueing network. Standard estimators have been seen to perform poorly when the network is heavily loaded. We introduce two new simulation estimators. The first provides substantial variance reductions in moderatelylo ..."
Abstract

Cited by 9 (7 self)
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We use simulation to estimate the steadystate performance of a stable multiclass queueing network. Standard estimators have been seen to perform poorly when the network is heavily loaded. We introduce two new simulation estimators. The first provides substantial variance reductions in moderatelyloaded networks at very little additional computational cost. The second estimator provides substantial variance reductions in heavy traffic, again for a small additional computational cost. Both methods employ the variance reduction method of control variates, and differ in terms of how the control variates are constructed.
The ODE method for stability of skipfree Markov chains with applications to MCMC
 Annals of Applied Probability
"... Fluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation and optimization. In this paper, some of these techniques are extended to a general class of skipfree Markov chains. As in the case of queueing ..."
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Cited by 5 (0 self)
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Fluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation and optimization. In this paper, some of these techniques are extended to a general class of skipfree Markov chains. As in the case of queueing models, a fluid approximation is obtained by scaling time, space and the initial condition by a large constant. The resulting fluid limit is the solution of an ordinary differential equation (ODE) in “most ” of the state space. Stability and finer ergodic properties for the stochastic model then follow from stability of the set of fluid limits. Moreover, similarly to the queueing context where fluid models are routinely used to design control policies, the structure of the limiting ODE in this general setting provides an understanding of the dynamics of the Markov chain. These results are illustrated through application to Markov chain Monte Carlo methods. The use of ordinary differential equations (ODE) to analyze Markov chains was first suggested by Kurtz (1970). This idea was later refined by Newell (1982), who introduced the socalled fluid approximations with applications to queueing networks. Since the 1990s, fluid models have been used to address delay in complex networks [Cruz (1991)] and bottleneck analysis [Chen and Mandelbaum (1991)]. The latter work followed an already extensive research program on diffusion approximations for networks [see Harrison
ADAPTIVE CONTROL VARIATES
"... Adaptive Monte Carlo methods are specialized Monte Carlo simulation techniques where the methods are adaptively tuned as the simulation progresses. The primary focus of such techniques has been in adaptively tuning importance sampling distributions to reduce the variance of an estimator. We instead ..."
Abstract
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Adaptive Monte Carlo methods are specialized Monte Carlo simulation techniques where the methods are adaptively tuned as the simulation progresses. The primary focus of such techniques has been in adaptively tuning importance sampling distributions to reduce the variance of an estimator. We instead focus on adaptive control variate schemes, developing asymptotic theory for the performance of two adaptive control variate estimators. The first estimator is based on a stochastic approximation scheme for identifying the optimal choice of control variate. It is easily implemented, but its performance is sensitive to certain tuning parameters, the selection of which is nontrivial. The second estimator uses a sample average approximation approach. It has the advantage that it does not require any tuning parameters, but it can be computationally expensive and requires the availability of nonlinear optimization software. 1
Variance Reduction in Simulation of Multiclass Processing Networks
, 2005
"... We use simulation to estimate the steadystate performance of a stable multiclass queueing network. Standard estimators have been seen to perform poorly when the network is heavily loaded. We introduce two new simulation estimators. The first provides substantial variance reductions in moderatelylo ..."
Abstract
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We use simulation to estimate the steadystate performance of a stable multiclass queueing network. Standard estimators have been seen to perform poorly when the network is heavily loaded. We introduce two new simulation estimators. The first provides substantial variance reductions in moderatelyloaded networks at very little additional computational cost. The second estimator provides substantial variance reductions in heavy traffic, again for a small additional computational cost. Both methods employ the variance reduction method of control variates, and differ in terms of how the control variates are constructed.
ADAPTIVE CONTROL VARIATES IN MONTE CARLO SIMULATION
, 2006
"... Monte Carlo simulation is widely used in many fields. Unfortunately, it usually requires a large amount of computer time to obtain even moderate precision so it is necessary to apply efficiency improvement techniques. Adaptive Monte Carlo methods are specialized Monte Carlo simulation techniques whe ..."
Abstract
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Monte Carlo simulation is widely used in many fields. Unfortunately, it usually requires a large amount of computer time to obtain even moderate precision so it is necessary to apply efficiency improvement techniques. Adaptive Monte Carlo methods are specialized Monte Carlo simulation techniques where the methods are adaptively tuned as the simulation progresses. The primary focus of such techniques has been in adaptively tuning importance sampling distributions to reduce the variance of an estimator. We instead focus on adaptive methods based on control variate schemes. In this dissertation we introduce two adaptive control variate methods where a family of parameterized control variates is available, and develop their asymptotic properties. The first method is based on a stochastic approximation scheme for identifying the optimal choice of control variate. It is easily implemented, but its performance is sensitive to certain tuning parameters, the selection of which is nontrivial. The second method uses a sample average approximation approach. It has the advantage that it does not require any tuning parameters, but it can be computationally