Variance Reduction Techniques on Generating M/M/1 Processes in Simulation Output Analysis

Observations from steady-state M/M/1 processes are often used by simulation-methodology researchers conducting Monte Carlo performance evaluations of output analysis, variance reduction, and optimization. The classical method for generating data from M/M/1 processes requires two random number stream...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 58; no. 4; pp. 1035 - 1040
Main Authors Song, W. T., Mingchang Chih, Samping Chuang
Format Journal Article
LanguageEnglish
Published New York IEEE 01.04.2013
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Computer simulation
Conduction
Correlation
Equations
Inverse-transformation
M/M/1 processes
Mathematical analysis
Mathematical model
Newton method
Optimization
Queueing analysis
Random numbers
Reduction
Silicon
simulation output analysis
Steady-state
Streams
Variance
variance reduction
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Summary:Observations from steady-state M/M/1 processes are often used by simulation-methodology researchers conducting Monte Carlo performance evaluations of output analysis, variance reduction, and optimization. The classical method for generating data from M/M/1 processes requires two random number streams. Motivated by the need for variance reduction in simulation experiments, we propose inverse-transformation algorithms for generating M/M/1 processes, including waiting times in queue (M/M/1-QT) and in system (M/M/1-ST), using a single random number stream. Moreover, we propose analytical results for computing the variance of the sample mean from M/M/1 processes. The proposed method for generating processes for the M/M/1-QT and the M/M/1-ST is superior (in terms of statistical effectiveness; i.e., variance reduction) to the corresponding classical methods using two random number streams. Moreover, the proposed generation method for M/M/1-QT is also superior to the classical method in terms of computational efficiency. Finally, although the proposed M/M/1-ST generation method is not as computationally efficient as the classical technique, it does have the same computational efficiency as the classical method if a parallel computing scheme is adopted with the Newton's search method.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2012.2231553