An Enhanced Two-Stage Selection Procedure
E. Jack Chen and W. David Kelton (University of Cincinnati)
This paper discusses implementation of a two-stage procedure to determine the simulation run length for selecting the best of k designs. We purpose an Enhanced Two-Stage Selection (ETSS) procedure. The number of additional replications at the second stage for each design is determined by both the variances of the sample means and the differences of the sample means of alternative designs. We show that the ETSS procedure gives valid selections with significantly reduced simulation replications compared to Rinott's procedure. An experimental performance evaluation demonstrates the validity of the ETSS procedure.
Optimal Selection Probability in the Two-Stage
Nested Partitions Method for Simulation-Based Optimization
Sigurdur Ólafsson and Nithin Gopinath (Iowa State University)
We investigate a new algorithm for simulation-based optimization where the number of alternatives is finite but very large. This algorithm draws on recent work in adaptive random search and from ranking-and-selection. We show how the ranking-and-selection approach can significantly improve performance of the random search and demonstrate the importance of the probability of correct selection.
Improved Decision Processes through Simultaneous
Simulation and Time Dilation
Paul Hyden (Cornell University) and Lee Schruben (University of California at Berkeley)
Simulation models are often not used to their full potential in the decision-making process. The default simulation strategy of simple serial replication of fixed length runs means that we often waste time generating information about uninteresting models and we only provide a decision at the very end of our study. New simulation techniques such as simultaneous simulation and time dilation have been developed to produce improved decisions at any time with limited or even reduced demands on analysts. Furthermore, we have the tools to determine whether a study should be terminated early or extended based on the demands of the decision-responsible managers and the time-crunched analysts. By collecting information from multiple models at the same time and using this information to continuously update the allocation of finite computational resources, we are able to more effectively leverage every minute of calendar time toward making the best choice. Strategies and tactics are discussed and highlighted through the implementation and analysis of a job shop model. Target success probabilities are achieved faster while achieving goals in study length flexibility at low cost to analyst time.
Finding Important Independent Variables through
Screening Designs: A Comparison of Methods
Linda Trocine and Linda C. Malone (University of Central Florida)
Once a simulation model is developed, designed experiments may be employed to efficiently optimize the system. Designed experiments are used on "real" production systems as well. The first step is to screen for important independent variables. Several screening methods are compared and contrasted in terms of efficiency, effectiveness, and robustness. These screening methods range from the classical factorial designs and two-stage group screening to new, more novel designs including sequential bifurcation and iterated fractional factorial designs (IFFD). Conditions for the use of the methods are provided along with references on how to use them.
A Comparison of Five Steady-State Truncation Heuristics
K. Preston White, Jr. (University of Virginia), Michael J. Cobb (Univeristy of Virginia) and Stephen C. Spratt (St. Onge Company)
We compare the performance of five well-known truncation heuristics for mitigating the effects of initialization bias in the output analysis of steady-state simulations. Two of these rules are variants of the MSER heuristic studied by White (1997); the remaining rules are adaptations of bias-detection tests based on the seminal work of Schruben (1982). Each heuristic was tested in each of a 168 different experiments. Each experiment comprised multiple tests on different realizations of the sample path of a second-order autoregressive process with known (deterministic) bias function. Different experiments employed alternative process parameters, generating a range of damped and underdamped stochastic responses. These were combined with alternative damped, underdamped, and mean shift bias functions. The performance of each rule was evaluated based on the ability of the rule to remove bias from the mean estimator for the steady-state process. Results confirmed that four of the five rules were effective and reliable, consistently yielding truncated sequences with reduced bias. In general, the MSER heuristics outperformed the three rules based on bias detection, with Spratt’s (1998) MSER-5 the most effective and robust choice for a general-purpose method.
A Perspective of Batching Methods in a Simulation
Environment of Multiple Replications in Parallel
Edjair Mota (University of Amazonas), Adam Wolisz (Technical University of Berlin) and Krysztof Pawlikowski (University of Canterbury)
Discrete event simulation is frequently time-consuming either because modern dynamic systems, such as telecommunication networks, are becoming increasingly complex and/or a great number of observations is required to yield reasonably accurate results. An interesting approach to reduce the time duration of simulation is that of concurrently running multiple replications in parallel (MRIP) on a number of processors connected via networking and averaging the results adequately. We present the results of our research on the suitability of batch-means-based procedures in such distributed stochastic simulation.
Nonparametric Adaptive Importance Sampling for Rare Event
Yun Bae Kim and Deok Seon Roh (Sung Kyun Kwan University) and Myeong Yong Lee (Korea Telecom R&D Group)
Simulating rare events in telecommunication networks such as estimation for cell loss probability in Asynchronous Transfer Mode (ATM) networks requires a major simulation effort due to the slight chance of buffer overflow. Importance Sampling (IS) is applied to accelerate the occurrence of rare events. Importance Sampling depends on a biasing scheme to make the estimator from IS unbiased. Adaptive Importance Sampling (AIS) employs an estimated sampling distribution of IS to the system of interest during the course of simulation. In this study, we propose a Nonparametric Adaptive Importance Sampling (NAIS) technique, a non-parametrically modified version of AIS, and estimate the probability of rare event occurrence in an M/M/1 queueing model. Compared with classical Monte Carlo simulation and AIS, the computational efficiency and variance reductions gained via NAIS are reasonable. A possible extension of NAIS with regards to random number generation is also discussed.
Analyzing Transformation-Based Simulation
Maria de los A. Irizarry (University of Puerto Rico), Michael E. Kuhl (Louisiana State University) and Emily K. Lada, Sriram Subramanian, and James R. Wilson (North Carolina State University)
We present a technique for analyzing a simulation meta-model that has been constructed using a variance-stabilizing transformation. To compute a valid confidence interval for the expected value of the original simulation response at a selected factor-level combination (design point), we first compute the corresponding confidence interval for the transformed response at that factor-level combination and then untransform the endpoints of the resulting confidence interval. Taking the midpoint of the untransformed confidence interval as our point estimator of the expected simulation response at the selected factor-level combination and approximating the variance of this point estimator via the delta method, we formulate an approximate two-sample Student t-test for validating our metamodel-based estimator versus the results of making independent runs of the simulation at the selected factor-level combination. We illustrate this technique in a case study involving the design of a manufacturing cell, and we compare our results with those of a more conventional approach to analyzing transformed-based simulation meta-models. A Monte Carlo performance evaluation shows that significantly better confidence-interval coverage is maintained with the proposed procedure over a wide range of values for the residual variance of the transformed metamodel.
On the Use of Control Variates in the
Simulation of Medium Access Control Protocols
Andrés Suárez-González, Cándido López-García, José C. López-Ardao, and Manuel Fernández-Veiga (Universidade de Vigo)
Simulation is an essential tool for performance evaluation of communication networks. We are interested in the waiting time W of packets. The Control Variates method takes profit of the knowledge about another stochastic process strongly correlated with W to reduce the uncertainty in the estimation of its mean. We analyze the usefulness of the cycle time as a control stochastic process for Medium Access Control (MAC) protocols with polling service discipline, showing its potential and drawbacks. We propose a control variate that overcomes the disadvantages of cycle time and show its behavior in a case study. This new control variate will also be useful in the case of other MAC protocols.
Multi-Response Simulation Optimization using
Stochastic Genetic Search within a Goal Programming
Felipe F. Baesler and José A. Sepúlveda (University of Central Florida)
This study presents a new approach to solve multi-response simulation optimization problems. This approach integrates a simulation model with a genetic algorithm heuristic and a goal programming model. The genetic algorithm technique offers a very flexible and reliable tool able to search for a solution within a global context. This method was modified to perform the search considering the mean and the variance of the responses. In this way, the search is performed stochastically, and not deterministically like most of the approaches reported in the literature. The goal programming model integrated with the genetic algorithm and the stochastic search present a new approach able to lead a search towards a multi-objective solution.
A Practical Approach to Sample-Path Simulation
Michael C. Ferris, Todd S. Munson, and Krung Sinapiromsaran (University of Wisconsin)
We propose solving continuous parametric simulation optimizations using a deterministic nonlinear optimization algorithm and sample-path simulations. The optimization problem is written in a modeling language with a simulation module accessed with an external function call. Since we allow no changes to the simulation code at all, we propose using a quadratic approximation of the simulation function to obtain derivatives. Results on three different queueing models are presented that show our method to be effective on a variety of practical problems.
Simulation Optimization Using Tabu
Berna Dengiz and Cigdem Alabas (Gazi University)
Investigation of the performance and operation of complex systems in manufacturing or other environments, analytical models of these systems become very complicated. Because of the complex stochastic characteristic of the systems, simulation is used as a tool to analyze them. The trust of such simulation analysis usually is to determine the optimum combination of factors that effect the considered system performance. The purpose of this study is to use a tabu search algorithm in conjunction with a simulation model of a JIT system to find the optimum number of kanbans.