##
**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
PDF
BibTeX
XML
Cite

\textit{J. W. Crawford} and \textit{T. J. Gallwey}, Eur. J. Oper. Res. 124, No. 3, 571--590 (2000; Zbl 0968.62034)

Full Text:
DOI

### References:

[1] | AndrĂ©asson, I.J., 1972. Antithetic methods in queueing simulations, Technical report NA 72.58, Royal Institute of Technology, Stockholm |

[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) |

[5] | Crawford, J.W., Gallwey, T.J., 1995. An empirical evaluation of the effect of some factors on the design of computer simulation studies. In: Dar-El, E.M., Karni, R., Herer, Y.T. (Eds.), Proceedings of the 13th International Conference on Production Research, Freund Publishing House, 432-434 |

[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) |

[10] | Hammersly, J.M., Handscomb, D.C., 1964. Monte Carlo Methods, Methuen, London |

[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 |

[14] | Kleijnen, J.P.C., 1971. Variance reduction techniques in simulation, Unpublished dissertation, Katholieke Hogeschool, Tilburg, Netherlands |

[15] | Kleijnen, J.P.C., 1975. Statistical techniques in simulation. Part II, Marcel Dekker, New York · Zbl 0345.65002 |

[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 |

[17] | Law, A.M., Kelton, W.D., 1991. Simulation Modeling and Analysis, 2nd ed. McGraw-Hill, New York · Zbl 0489.65007 |

[18] | Neelamkavil, F., 1987. Computer simulation and modelling, Wiley, New York |

[19] | Nelson, B.L., 1987. Variance reduction for simulation practitioners. In: Thesen, A., Grant, H., Kelton, W.D. (Eds.), Proceedings of the Winter Simulation Conference, 43-51 |

[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 |

[24] | Schruben, L.W., Margolin, B.H, 1978. Pseudorandom number assignment in statistically designed simulation and distribution sampling experiments. JASA 73, 504-519 · Zbl 0386.62010 |

[25] | Tocher, K.D., 1963. The Art of Simulation, English University Press, London |

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

[27] | Welch, P.D., 1981. On the problem of the initial transient in steady-state simulation, IBM Watson Research Centre, Yorktown Heights, NY |

[28] | Welch, P.D., 1983. The statistical analysis of simulation results, In: Lavenberg, S.S., (Ed.), The Computer Performance Modeling Handbook, Academic Press, New York, 268-328 |

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

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.