S.G. Henderson, Variance reduction via an approximating Markov process, Ph.D. thesis, Stanford University, Stanford, CA, USA (1997).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the optimizing # is again consistent with theoretical results obtained for the CBM model. The plots shown in Figure 9 reveal significant variance even though the time horizon was large: T = 510 samples for each value of #. Variance in simulation of queues is typically high in moderate tra#c [1, 53, 25, 27, 28]. The variance is more apparent in Figure 9 (b) due to the narrow range of values on the vertical axis. 6.3 Numerical results for Case III We now consider Case III using the rates seen previously in (25) The loads at the two machines are # 1 = respectively. The theory in Case III is far ....

S.G. Henderson. Variance Reduction Via an Approximating Markov Process. PhD thesis, Stanford University, Stanford, California, USA, 1997.

.... leads to ner results: 1) The solution to Poisson s equation is central to optimal control where f is a one step cost function, and f is called the relative value function [5, 6, 1, 16, 12] 2) Approximate solutions to Poisson s equation lead to direct performance bounds (estimates of ) [8, 15, 7, 3, 4]. 3) The solution to Poisson s equation allows us to construct the useful martingale: M(t) t 1 X i=0 f(X(i) f(X(t) t 3 This leads to the central limit theorem, 1 p N N 1 X 0 (f(X(t) d N(0; 2 ) where 2 = 2 ( f(f ) f ) 2 ) Hence Poisson s ....

.... the useful martingale: M(t) t 1 X i=0 f(X(i) f(X(t) t 3 This leads to the central limit theorem, 1 p N N 1 X 0 (f(X(t) d N(0; 2 ) where 2 = 2 ( f(f ) f ) 2 ) Hence Poisson s equation provides tools for addressing performance of simulators [3]. Example M=M=1 queue When the arrival stream is renewal, and the service times are i.i.d. then the waiting time for a simple queue can be modeled as a Markov chain with state space X = IR . The dynamics take the form of a one dimensional linear state space model, where the state space is ....

Henderson, S. G. Variance Reduction Via an Approximating Markov Process. Ph.D. thesis. Department of Operations Research, Stanford University. Stanford, California, USA, 1997.

....we obtain a time average variance of zero. Of course, computing t involves a computation of J , so this approach is nonsensical If however an approximation g to h can be found, then the choice t = P g (x t ) g(x t ) will lead to reduced variance if the approximation is suciently tight [24]. This is a useful result for our purposes since we will discover such approximations when we attempt to solve some optimization problems below. 1.3.3 Examples In this chapter we will restrict ourselves to two general examples: the linear state space model, and a family of network models. In ....

Henderson, S. G. Variance Reduction Via an Approximating Markov Process. Ph.D. thesis. Department of Operations Research, Stanford University. Stanford, California, USA, 1997.

....component of only. If the function h is integrable, then ( h ) 0, and so one might use the consistent estimator b c (n) b (n) 1 n n 1 X i=0 h ( i) 4. 8) This approach can lead to substantial variance reductions, especially in heavy trac, when applied to the GI G 1 queue [20]. In [21] these ideas are extended to network models. First note that the estimator (4.8) will have a variance of zero when h solves the Poisson equation h = c . While this choice is not computable in general, we can approximate h by the uid value function, V (y) Z 1 0 c( t; x) ....

Henderson, S. G. Variance Reduction Via an Approximating Markov Process. Ph.D. thesis. Department of Operations Research, Stanford University. Stanford, California, USA, 1997.

No context found.

S.G. Henderson. Variance Reduction Via an Approximating Markov Process. PhD thesis, Department of Operations Research, Stanford University, Stanford, California, USA, 1997.

....simulation, obtaining useful but modest improvements in performance. Andrad ottir et al. 1993) considered discrete time Markov chains on a finite state space, and obtained variance reduction in steady state simulations. Their approach is closely 2 related to the theory we present in Section 5. Henderson (1997) develops the theory presented here in the context of steady state simulation, and applies it to the simulation of various processes associated with the single server queue. In the first five sections of this paper we show how to define approximating martingales for a variety of performance ....

....variables to the state space in order to ensure that the resulting process is Markov. For such processes, the identification and application of approximating martingales is not as easy as it is for the processes we consider here, but it can still be done. This issue, and others, are addressed in Henderson (1997) and Henderson and Glynn (1998) Further comments on this issue are also given in Section 8. Section 8 also demonstrates that our approach may be applied in ways that at first, may not appear obvious. In particular, we discuss how the approximating martingale may be turned on and off , depending ....

[Article contains additional citation context not shown here]

Henderson, S. G. (1997). Variance Reduction Via an Approximating Markov Process. Ph.D. Thesis, Department of Operations Research, Stanford University, Stanford CA. Also available at http://wwwor.

....result (see Theorem 2) holds for multiclass queueing networks with a single station, and we believe the same is true of more complicated networks. Indeed, in simulation experiments, we have seen exactly this effect, namely that the TAVC grows rapidly as the network encounters heavy traffic. 3 In [11], a new class of estimators was introduced that yielded substantial variance reductions, especially in heavy traffic, when applied to the GI G 1 queue. This paper is an outgrowth of [12] where we attempted to extend the ideas in [11] to the simulation of multiclass queueing networks. Although ....

....grows rapidly as the network encounters heavy traffic. 3 In [11] a new class of estimators was introduced that yielded substantial variance reductions, especially in heavy traffic, when applied to the GI G 1 queue. This paper is an outgrowth of [12] where we attempted to extend the ideas in [11] to the simulation of multiclass queueing networks. Although our presentation concentrates on the estimation of the mean steady state number of customers (of all classes) in the system, our methods may be tailored to the steady state estimation of any linear function of the individual customer ....

[Article contains additional citation context not shown here]

Henderson, S. G. (1997). Variance Reduction Via an Approximating Markov Process. Ph.D. thesis. Department of Operations Research, Stanford University. Stanford, California, USA.

No context found.

S.G. Henderson, Variance reduction via an approximating Markov process, Ph.D. thesis, Stanford University, Stanford, CA, USA (1997).

No context found.

S.G. Henderson. Variance Reduction Via an Approximating Markov Process. PhD thesis, Stanford University, Stanford, California, USA, 1997.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC