A classical problem of stochastic simulation is how to estimate the variance of the sample mean from dependent but stationary outputs. Traditional estimators of the variance of the sample mean require specification of the simulation
run length a priori. To our knowledge, the dynamic non-overlapping batch means (DNBM) and dynamic partial overlapping batch means (DPBM) are the only two existing variance estimators without assuming that the simulation run
length (data size) is known in advance.
Obtaining good estimators of the variance of the sample mean without assuming that the data size is known in advance is the primary motivation of the author's dissertation research. The research encompasses five areas:
1. The creation of improving the DPBMin terms of the storage space.
2. The creation of proposing the 100(1−w−1)%DOBM, which is a generalization of DNBM and DPBM.
3. The creation of obtaining finite-memory algorithms to extend DPBM algorithm to reflect the correlation structure of the data.
4. The investigation of developing MSE-optimalDPBM algorithms to estimate the variance of the sample via estimating the optimal batch size of the estimator.
5. In addition, we apply simulation to study a physical examination service to
improve the system efficiency.

Aharonson-Daniel, L., Paul, R. J., andHedley,A. J. (1996)Management of queuesin out-patient departments: the use of computer simulation. Journal of Management inMedicine, 10, 50-58.

Aktaran-Kalaycı, T., Alexopoulos, C., Argon, N. T., Goldsman, D. and Wilson, J. R. (2007) Exact expected values of variance estimators for simulation. Naval Research Logistics, 54, 397–410.

Babes, M. and Sarma, G. V. (1991) Out-patient queues at the Ibn-Rochd Health Centre. Journal of the Operational Research Society, 42, 845-855.

Bartlett, M. S. (1946) On the Theoretical Specification of Sampling Properties of Autocorrelated Time Series. J. Royal Statist. Soc. 108, 27–41.

Box, G. E. P. and Jenkins, G. M. (1976) Series Analysis, Forecasting, and Control. Holden-Day, San Francisco.

Chen, E. J. and Kelton, W. D. (2003) Determining Simulation Run Length with the Runs Test, SimulationModelling Practice and Theory 11 (3-4): 237–250.

Chen, E. J. and Kelton, W. D. (2007) A Procedure for Generating Batch-Means Confidence Intervals for Simulation: Checking Independence and Normality, Simulation: Transactions of The Society forModeling and Simulation International 83: 683-694.

Clague, J. E., Reed, P. G., Barlow, J., Rada, R., Clarke, M., and Edwards, R. H. T. (1997) Improving outpatient clinic efficiency using computer simulation. International Journal of Health Care Quality Assurance, 10, 197-201.

Conway, R.W. (1963) Some tactical problems in digital simulation. Management Science, 6, 92–110.

Crane, M. A. and Iglehart, D. L. (1975) Simulating stable stochastic systems, III: regenerative process and discrete-event simulations. Operations Research, 23, 33–45.

Dull, P. andHaines,D. J. (2003)Methods for teaching physical examination skills to medical students. Family Medicine, 35, 343-348.

Edwards, R. H., Clague, J. E., Barlow, J., Clarke, M., and Reed, P.G. (1994) Operations research survey and computer simulation of waiting times intomedical outpatient clinic structures. Health Care Analysis, 2, 164-169.

England, W. and Roberts, S. D. (1978) Applications of computer simulation in health care. Proceedings of theWinter Simulation Conference, 665–677.

Ferguson, N.M., Cummings, D.A., Fraser, C., Cajka, J.C., Cooley, P.C. and Burke, D.S. (2006) Strategies for mitigating an influenza pandemic, Nature, 442, 448–452.

Fishman, G. S. and Yarberry, L. S. (1997) An implementation of the batch means method, INFORMS Journal on Computing, 9, 296–310.

Fone, D., Hollinghurst, S., Temple, M., Round, A., Lester, N., Weightman, A., Roberts, K., Coyle, E., Bevan, G. and Palmer, S. (2003) Systematic review of the use and value of computer simulation modeling in population health and health care delivery. Journal of Public HealthMedicine, 25, 325–335.

Friedman, L.W., and Pressman, I. (1988) Themetamodel in simulation analysis: Can it be trusted? Journal of the Operational Research Society, 39, 939-948.

Glynn, P. W. and Iglehart, D. L. (1986) Estimation of steady-state central moments by the regenerative method of simulation. Operations Research Letters, 5, 271–276.

Glynn, P.W. and Iglehart,D. L. (1990) Simulation output analysis using standardized time series. Mathematics of Operations Research, 15, 1–16.

Goldsman, D. and Schmeiser, B.W. (1997) Computational efficiency of batching method, Proceedings of theWinter Simulation Conference, 202–207.

Goldsman, D., Nelson, B. L., and Schmeiser, B. (1991)Methods for selecting the best system. Proceedings of theWinter Simulation Conference, 177-186.

Hillier, F. S., and Lieberman, G. J. (2001) Introduction to Operations Research, Seventh Edition. New York: McGraw-Hill.

Heidelberger, P. and Welch, P. D. (1981) A spectral method for confidence interval generation and run length control in simulation. Communication of the ACM, 24, 233–245.

Indra, R., Patil, S. S., Joshi, R., Pai,M., and Kalantri, S. P. (2004) Accuracy of physical examination in the diagnosis of hypothyroidism: a cross-sectional double
blind study. Journal of PostgraduateMediciney, 50, 7-10.

Jenvald, J.,Morin,M., Timpka, T. and Eriksson, H. (2007) Simulation as decision support in pandemic influenza preparedness and response. Proceedings of ISCRAM, 295–304.

Jun J. B., Jacobsen, S. H. and Swisher, J. R. (1999) Application of discrete-event simulation in health care clinics: a survey. Journal of the Operational Research
Society, 50, 109–123.

Kalton, A. G., Singh, M. R., August, D. A., Parin, C. M., and Othman, E. J. (1997) Using simulation to improve the operational efficiency of a multidisciplinary clinic. Journal of the Society for Health Systems, 5, 43-62.

Kelton, W. D., Sadowski, R. P., and Sturrock, D. T. (2006) Simulation with Arena, Fourth Edition. Boston, Massachusetts: McGraw-Hill.

Kleijnen, J.P.C (2007) DASE:Design and Analysis of Simulation Experiments, First Edition. NewYork: Springer.
Krahl,D. (2003) Extend: an interactive simulation tool. Proceedings of theWinter Simulation Conference, 188-196.

Kropp, D. H. and Carlson, R. C. (1977) Recursivemodeling of ambulatory health care settings. Journal ofMedical Systems, 1, 123–135.

Kwak, N. K., Kuzdrall, P. J., and Schmitz, H. H. (1976) The GPSS simulation of scheduling policies for surgical patients. Management Science, 22, 982-989.

Lall, A., Sekar, V., Ogihara, M., Xu, J., and Zhang, U. (2006) Data streaming algorithms for estimating entropy of network traffic. ACMSIGMETRICS/Performance Conference, 145–156.

Law, A.M. (2007) Simulation modeling and analysis. Boston, Massachusetts: McGraw-Hill.

Law, A. M. (2006) Simulation Modeling and Analysis with Expertfit Software, Fourth Edition. Boston,Massachusetts: McGraw-Hill.

Miller, D., Garza, J., Tuggle, D., Mantor, C., and Puffinbarger, N. (2006) Physical examination as a reliable tool to predict intra-abdominal injuries in braininjured
children. The American Journal of Surgery, 192, 738-742.

Meketon, M. S. and Schmeiser, B. W. (1984) Overlapping batch means: something for nothing? Proceedings of the Winter Simulation Conference, 227–230.

Montgomery, D. C. and Runger, G. C. (2006) Applied Statistics and Probability for Engineering. New York: JohnWiley & Sons, Inc., Third Edition.

Moran,M. S. (1975) The estimation of standard errors inMonte Carlo simulation experiments. Biometrika, 62, 1–4.

Nardone, D. A., James, K. E, and Finck, D. L. (1998) Impact of gowning on visit length and physical examinations. Journal of General InternalMedicine, 13, 489-490.

Nomden, J. G., Slagers, A. J, Bergman, G. J. D., Winters, J. C., Kropmans, T. J. B., and Dijkstra, P. U. (2009) Interobserver reliability of physical examination of
shoulder girdle. Manual Therapy, 14, 152-159.

Nordgren,W. B. (2003) Flexsim simulation environment. Proceedings of theWinter Simulation Conference,, 197-200.

Pedrosa, A. and Schmeiser, B.W. (1994) Estimating the variance of the sample mean: Optimal batch-size estimation and 1-2-1 overlapping batch means. Technical Report SMS94-3, School of Industrial Engineering, Purdue University,
West Lafayette, IN.

Podgorelec, V. and Kokol, P. (2001) Towards more optimal medical diagnosing with evolutionary algorithms. Journal ofMedical Systems, 25, 195-219.

Priestley, M. B. (1981) Spectral Analysis and Time Series. Academic Press, London. Raouf, A. and Ben-Daya, M. (1997) Outpatient clinic’s staffing: a case study. International
Journal of Health Care Quality Assurance, 10, 229-232.

Reilly, B. M. (2003) Physical examination in the care of medical inpatients: an observational study. The Lancet, 362: 1100-1105.

Salerno, D. F., Franzblau, A.,Werner, R. A., Chung, K. C., Schultz, S., Becker,M. P., and Armstrong, T. J. (2000) Reliability of physical examination of the upper
extremity among keyboard operators. American Journal of Industrial Medicine, 37, 423-430.

Schmeiser, B. W. (1982) Batch size effects in the analysis of simulation output. Operations Research, 30, 556–568.

Schruben, L. W. (1983) Confidence interval estimation using standardized time series. Operations Research, 31, 1090–1108.

Schruben, L. W. (1983) Simulation modeling with event graphs. Communications of the Association of Computing Machinery, 26, 957–963.

Schruben, L.W. (1990) Simulation graphicalmodeling and analysis (SIGMA) tutorial. Proceedings of theWinter Simulation Conference, 158–161.

Schwind, C. J., Boehler,M. L., Folse, R.,Dunnington,G, andMarkwell, S. J. (2001) Development of physical examination skills in a third-year surgical clerkship.
The American Journal of Surgery, 181, 338-340.

Shechter, S. M., Schaefer, A. J., Braithwaite, R. S. and Roberts, M. S. (2006) Increasing the efficient ofmonte carlo cohort simulationwith variance reduction techniques. Medical DecisionMaking, 26, 550–553.

Song, W.-M. T. (1988) Estimators of the variance of the sample mean: quadratic forms, optimal batch sizes, and linear combinations. Ph.D. Dissertation, School of Industrial Engineering, Purdue University,W. Lafayette, ind, USA.

Song, W.-M. T. (2007) A finite-memory algorithm for estimating the variance of the samplemean. IIE Transactions, 39, 703–711.

Song, W.-M. T. and Schmeiser, B. W. (1995) Optimal mean-squared-error batch size. Management Science, 41, 110–123.
Song,W.-M.T., and Schmeiser, B.W. (2009) Omitting Meaningless Digits in Point Estimates: The Probability Guarantee of Leading-Digit Rules, Operations Research, 57, 109-111.

Swain, J. J. (2005) “Gaming” reality: Biennial survey of discrete-event simulation software tools, OR/MS Today, December, 32, 44-55.

Vogt,W., Braun, S. L., Hanssmann, F., Liebl, F., Berchtold,G., Blaschke, H., Eckert, M., Hoffmann, G. E., and Klose, S. (1994) Realistic modeling of clinic
laboratory operation by simulation. Clinical Chemistry, 40, 922-928.

Welch, P. D. (1987) On the relationship between batchmeans, overlapping batch means and spectral estimation. Proceedings of the Winter Simulation Conference,
320–323.

Wilson, J. R. (1979) Variance reduction techniques. Ph.D. Dissertation, School of Industrial Engineering, Purdue University,West Lafayette, IN.

Wullink, G., Houdenhoven, M. V., Hans, E. W., Oostrum, J. M., Lans, M. and Kazemier, G. (2007) Closing emergency operating rooms improves efficiency. Journal of Medical Systems, 31, 543–546.

Yang, T.-K. (2001) Estimating the variance of sample mean with finite storage space. Master Thesis, Department of Industrial Engineering and EngineeringManagement, National Tsing Hua University, Hsinchu, ROC.

Yeh, Y. and Schmeiser, B.W. (2000) Simulation output analysis via dynamic batch means. Proceedings of theWinter Simulation Conference, 637–645.

Zhao, H., A. Lall,M. Ogrihara, O. Spatscheck, J.Wang, andWu, J. (2007) A data streaming algorithm for estimating entropies of OD flows. Proceedings of the ACM Internet Measurement Conference.