1,720,978 research outputs found
Improved design of queueing simulation experiments with highly heteroscedastic responses
No full textSimulation experiments for analysing the steady-state behaviour of queueing systems over a range of traffic intensities are considered, and a procedure is presented for improving their design. In such simulations the mean and variance of the response output can increase dramatically with traffic intensity; the design has to be able to cope with this complication. A regression metamodel of the likely mean response is used consisting of two factors, namely, a low-degree polynomial and a factor accounting for the exploding mean as the traffic intensity approaches its saturation. The best choice of traffic intensities at which to make simulation runs depends on the variability of the simulation output, and this variability is estimated using analytical heavy traffic results. The optimal numbers of customers simulated at each traffic intensity are built up using a multistage procedure. The asymptotic properties of the procedure are investigated theoretically. The procedure is shown to be robust and to be more efficient than more naive procedures. A result of note is that even when the range of interest includes high traffic intensities, the highest traffic load simulated should remain well away from its upper limit; but the number of customers simulated should be concentrated at the higher traffic intensities used. Empirical results are included for simulations of a single server queue with different priority rules and for a complicated queueing network. These results support the theoretical results, demonstrating that the proposed procedure can increase the accuracy of the estimated metamodel significantly compared with more naive methods
Optimal allocation of runs in a simulation metamodel with several independent variables.
No full textCheng and Kleijnen (Oper. Res. 47(5) (1999) 762) propose a very general regression metamodel for modelling the output of a queuing system. Its main limitations are that the regression function is based on a polynomial and that it can use only one independent variable. These limitations are removed here. We derive an explicit formula for the optimal way of assigning simulation runs to the different design points
Optimization by simulation metamodelling methods
No full textWe consider how simulation metamodels can be used to optimize the performance of a system that depends on a number of factors. We focus on the situation where the number of simulation runs that can be made is limited, and where a large number of factors must be included in the metamodel. Bayesian methods are particularly useful in this situation and can handle problems for which classical stochastic optimization can fail. We describe the basic Bayesian methodology, and then an extension to this that fits a quadratic response surface which, for function minimization, is guaranteed to be positive definite. An example is presented to illustrate the methods proposed in this paper
Resampling methods of analysis in simulation studies
Full text linkThis is an introductory tutorial on the statistical analysis of simulation output, but focusing on the (elementary) use of resam-pling, and related computer intensive techniques. The aspects covered are (i) input modeling (ii) output analysis (iii) model validation and (iv) model building and selection. The presentation will be very practically oriented including a fair number of real-time spreadsheet demonstrations. The demonstration worksheets will be made freely available online, and participants are actively encouraged to download them to try out the methods in their own simulation
Classification analysis for simulation of the duration of machine breakdowns
No full textMachine failure can have a significant impact on the throughput of manufacturing systems, therefore accuratemodelling of breakdowns in manufacturing simulation models is essential. Finite mixture distributions havebeen successfully used by Ford Motor Company to model machine breakdown durations in simulation modelsof engine assembly lines. These models can be very complex, with a large number of machines. To simplifythe modelling we propose a method of grouping machines with similar distributions of breakdown durations,which we call the Arrows Classification Method, where the Two-Sample Cram´er-von-Mises statistic is usedto measure the similarity of two sets of the data. We evaluate the classification procedure by comparing thethroughput of a simulation model when run with mixture models fitted to individual machine breakdowndurations; mixture models fitted to group breakdown durations; and raw data. Details of the methods andresults of the classification will be presented, and demonstrated using an exampl
Balancing bias and variance in the optimization of simulation models
No full textWe consider the problem of identifying the optimal point of an objective in simulation experiments where the objective is measured with error. The best stochastic approximation algorithms exhibit a convergence rate of n-1/6 which is somewhat different from the n-1/2 rate more usually encountered in statistical estimation. We describe some simple simulation experimental designs that emphasize the statistical aspects of the process. When the objective can be represented by a Taylor series near the optimum, we show that the best rate of convergence of the mean square error is when the variance and bias components balance each other. More specifically, when the objective can be approximated by a quadratic with a cubic bias, then the fastest decline in the mean square error achievable is n-2/3. Some elementary theory as well as numerical examples will be presente
Optimal pricing for perishable products
No full textIn many industrial settings, managers face the problem of establishing a pricing policy that maximises the revenue from selling a given inventory of items by a fixed deadline, with the full inventory of items being available for sale from the beginning of the selling period. This problem arises in a variety of industries, including the sale of fashion garments, flight seats, and hotel rooms. We present a family of continuous pricing functions for which the optimal pricing strategy can be explicitly characterised and easily implemented. These pricing functions are the basis for a general pricing methodology which is particularly well suited for application in the context of an increasing role for the Internet as a means to market goods and services
Tuberculosis epidemics driven by HIV: is prevention better than cure?
No full textObjective: To compare the benefits of tuberculosis (TB) treatment with TB and HIV prevention for the control of TB in regions with high HIV prevalence.Design and methods: A compartmental difference equation model of TB and HIV has been developed and fitted to time series and other published data using Bayesian methods. The model is used to compare the effectiveness of TB chemotherapy with three strategies for prevention: highly active antiretroviral therapy (HAART), the treatment of latent TB infection (TLTI) and the reduction of HIV transmission.Results: Even where the prevalence of HIV infection is high, finding and curing active TB is the most effective way to minimize the number of TB cases and deaths over the next 10 years. HAART can be as effective, but only with very high levels of coverage and compliance. TLTI is comparatively ineffective over all time scales. Reducing HIV incidence is relatively ineffective in preventing TB and TB deaths over 10 years but is much more effective over 20 years.Conclusions: In countries where the spread of HIV has led to a substantial increase in the incidence of TB, TB control programmes should maintain a strong emphasis on the treatment of active TB. To ensure effective control of TB in the longer term, methods of TB prevention should be carried out in addition to, but not as a substitute for, treating active cases
A practical introduction to analysis of simulation output data
No full textThe tutorial will be used to introduce some basic techniques for analysing the output of stochastic simulation models. Using examples, we will describe methods for determining the optimal warm-up length and number of replications as well as introducing ways of using simulation to compare different systems
Validation of trace-driven simulation models: bootstrap tests
Full text linkTrace-driven (or correlated inspection) simulation means that the simulated and the real systems have some common inputs (say, historical arrival times) so that the two systems' outputs are cross-correlated. To validate such a simulation, this paper focuses on the difference between the average simulated and real responses. To evaluate this validation statistic, the paper develops a novel bootstrap technique--based on replicated runs. This validation statistic and the bootstrap technique are evaluated in extensive Monte Carlo experiments with specific single-server queues. These experiments show acceptable Type-I and Type-II error probabilities
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