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**Bias and variance reduction in computer simulation studies.**
*(English)*
Zbl 0968.62034

Summary: The research of several authors was extended to a complex queueing model with eleven responses. Warming-up the system, antithetic variates, and their joint applications, were compared with crude sampling. Emphasis was placed on constructed confidence intervals as opposed to the performance of point estimates. Performance was evaluated by means of the coverage probability and the change in confidence interval widths; the results differ from those of the earliest studies. The application of a warm-up period reduced bias; however, this reduction in bias was accompanied by a large increase in the confidence interval widths. Antithetic variates were employed in an attempt to reduce, or eliminate, any increases in confidence interval width caused by applying a warm-up period. The success of the techniques was found to be dependent on the type of model response that was being analysed.

### MSC:

62F25 | Parametric tolerance and confidence regions |

65C99 | Probabilistic methods, stochastic differential equations |

90B22 | Queues and service in operations research |

### Keywords:

discrete event simulation; steady-state; bias reduction; variance reduction; complex systems
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\textit{J. W. Crawford} and \textit{T. J. Gallwey}, Eur. J. Oper. Res. 124, No. 3, 571--590 (2000; Zbl 0968.62034)

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### References:

[2] | Cheng, R. H.C., A note on the effect of initial conditions on a simulation run, Operational Research Quarterly, 27, 2, 467-470 (1976) |

[3] | Cheng, R. H.C., Antithetic variate methods for the simulation of processes with peaks and troughs, European Journal of Operational Research, 27, 227-236 (1984) · Zbl 0524.65005 |

[4] | Conway, R. W., Some tactical problems in digital simulation, Management Science, 10, 47-61 (1963) |

[6] | Ernfield, S.; Ben-Tuvia, S., The efficiency of statistical simulation procedures, Technometrics, 4, 257-275 (1962) · Zbl 0111.16004 |

[7] | Fishman, G. S., Bias considerations in simulation experiments, Operations Research, 20, 785-790 (1972) · Zbl 0242.62035 |

[8] | Fishman, G. S., Statistical analysis for queueing simulations, Management Science, 20, 363-369 (1973) · Zbl 0317.62074 |

[9] | Halton, J. H.; Handscomb, D. C., A method for increasing the efficiency of monte carlo integration, Journal of the Association for Computing Machinery, 4, 329-340 (1957) |

[11] | Hammersly, J. M.; Morton, K. W., A new Monte Carlo technique: Antithetic variates, Proceedings of the Cambridge Philosophical Society, 52, 449-475 (1956) · Zbl 0071.35404 |

[12] | Harling, J., Simulation techniques in operations research, Operational Research Quarterly, 9, 9-21 (1958) |

[13] | Kelton, W. D.; Law, A. M., An analytical evaluation of alternative strategies in steady-state simulation, Operations Research, 32, 169-184 (1984) · Zbl 0532.65100 |

[16] | Law, A. M., Confidence intervals in discrete event simulation: A comparison of replication and batch means, Naval Research Logistics Quarterly, 24, 667-678 (1977) · Zbl 0415.62065 |

[20] | Nelson, B. L., Variance reduction in the presence of initial-condition bias, IIE Transactions, 22, 340-350 (1990) |

[21] | Roach, W.; Wright, R., Optimal antithetic sampling plans, Journal of Statistics and Computer Simulation, 5, 99-114 (1977) · Zbl 0347.62011 |

[22] | Schruben, L. W.; Singh, H.; Tierney, L., Optimal tests for initialisation bias in simulation output, Operations Research, 31, 1167-1178 (1983) · Zbl 0538.62075 |

[23] | Sullivan, R. S.; Hayya, J. C.; Schaul, R., Efficiency of the antithetic variate method for simulating stochastic networks, Management Science, 28, 5, 563-572 (1982) · Zbl 0484.65089 |

[26] | Turnquist, M. A.; Sussman, J. M., Toward guidelines for designing experiments in queueing simulation, Simulation, 28, 137-144 (1977) · Zbl 0352.68124 |

[29] | Wilson, J. R.; Pritsker, A. A.B., A survey of research on the simulation start-up problem, Simulation, 31, 55-58 (1978) |

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