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Time-dependent queueing network approximations as simulation external control variates. (English) Zbl 0815.90075

Summary: A strategy for efficient evaluation of a complex stochastic model’s performance is to use a simpler model’s known performance as an approximation. Another strategy is to simulate using the simpler model’s known performance as an external control variate. We combine these two strategies. We also relax the assumption that the simpler model’s performance is known exactly by introducing mean-squared-error optimal control variates.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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[1] Clark, G. M., Use of Polya distributions in approximate solutions to nonstationary M/M/s queues, Commun. ACM, 24, 206-218 (1981)
[2] Gaver, D. P.; Shedler, G. S., Control variable methods in the simulation of multiprogrammed computer systems, Naval Res. Logist. Quart., 18, 435-450 (1971)
[3] Goldsman, D. M.; Nelson, B. L.; Schmeiser, B. W., Methods for selecting the best system, (Nelson, B. L.; Kelton, W. D.; Clark, G. M., Proc. Winter Simulation Conf. (1991)), 177-186
[4] Johnson, M. A.; Taaffe, M. R., An investigation of phase-distribution moment-matching algorithms for use in queueing models, Queueing Systems — Theory Appl., 8, 129-148 (1991) · Zbl 0733.60106
[5] Lavenberg, S. S.; Moeller, T. L.; Welch, P. D., Statistical results on control variables with application to queuing network simulation, Oper. Res., 30, 182-202 (1982) · Zbl 0481.90024
[6] Lavenberg, S. S.; Welch, P. D., A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations, Management Sci., 27, 322-335 (1981) · Zbl 0452.65004
[7] Nelson, B. L.; Schmeiser, B. W., Decomposition of some well-known variance reduction techniques, J. Statist. Comput. Simulation, 23, 183-209 (1986)
[8] Nelson, B. L., A perspective on variance reduction in dynamic simulation experiments, Commun. Statist. B — Simulation and Comput., 16, 385-426 (1987) · Zbl 0627.65149
[9] Nelson, B. L., On control variate estimators, Comput. and Oper. Res., 14, 219-225 (1987) · Zbl 0628.93063
[10] Nelson, B. L., Batch size effects on the efficiency of control variates in simulation, Euro. J. Oper. Res., 43, 184-196 (1989) · Zbl 0679.62102
[11] Nelson, B. L., Control-variate remedies, Oper. Res., 38, 974-992 (1990) · Zbl 0731.62071
[12] Ong, K. L.; Taaffe, M. R., Approximating nonstationary Ph \((t)/M(t)/s/c\) queueing systems, Ann. Oper. Res., 8, 103-116 (1987)
[13] Ong, K. L.; Taaffe, M. R., Approximating Ph \((t)\)/Ph \((t)/1/c\) nonstationary queueing systems, Math. Comput. Simulation, 30, 441-452 (1988) · Zbl 0664.60100
[14] Ong, K. L.; Taaffe, M. R., Nonstationary queues with interrupted Poisson arrivals and unreliable/repairable servers, Queueing Systems: Theory and Appl., 4, 27-46 (1989) · Zbl 0664.60094
[15] Rothkopf, M. H.; Oren, S. S., A closure approximation for the nonstationary M/M/\(s\) queue, Management Sci, 25, 522-534 (1979) · Zbl 0427.90042
[16] Schmeiser, B. W.; Taaffe, M. R., Correlated decomposition and simulation of time-dependent queueing networks: Fortran 77 code, (Technical Report 91-15 (1991), Department of Operations and Management Science, University of Minnesota)
[17] Schmeiser, B. W.; Taaffe, M. R., Correlated decomposition for analyzing dynamic stochastic systems, (Klutke, G. A.; Mitta, D. A.; Nnajii, B. O.; Seiford, L. M., Proc. 1st IE Research Conf. (1992)), 457-462
[18] Sharon, A. P.; Nelson, B. L., Analytic and external control variates for queueing network simulation, J. Oper. Res. Soc., 39, 595-602 (1988)
[19] Swain, J. J.; Schmeiser, B. W., Control variates for Monte Carlo analysis of nonlinear statistical models I: Overview, Commun. Statist. B — Simulation Comput., 18, 1011-1036 (1989) · Zbl 0695.62150
[20] Taaffe, M. R., Approximating nonstationary queueing models, (Ph.D. Dissertation (1982), Department of Industrial and Systems Engineering, The Ohio State University) · Zbl 0627.90035
[21] Taaffe, M. R.; Clark, G. M., Approximating nonstationary queueing systems, (Highland, H. J.; Chao, Y. W.; Madrigal, O. S., Proc. Winter Simulation Conf. (1982)), 9-13
[22] Taaffe, M. R.; Clark, G. M., Approximating nonstationary two-priority nonpreemptive queueing systems, Naval Res. Logist., 35, 125-145 (1988) · Zbl 0627.90035
[23] Taaffe, M. R.; Horn, S. A., External control variance reduction methods for nonstationary simulation experimentation, (Roberts, S. D.; Banks, J.; Schmeiser, B. W., Proc. Winter Simulation Conf. (1983)), 341-343
[24] Taaffe, M. R.; Ong, K. L., Approximating time-dependent non-exponential queues, (Sheppard, S.; Pooch, U. W.; Pegden, C. D., Proc. Winter Simulation Conf. (1984)), 175-178
[25] Whitt, W., The queueing network analyzer, Bell Systems Tech. J., 62, 2779-2815 (1983)
[26] Whitt, W., Performance of the queueing network analyzer (QNA), Bell Systems Tech. J., 62, 2817-2843 (1983)
[27] Wilson, J. R., Variance reduction techniques for digital simulation, J. Math. Management Sci., 4, 277-312 (1984) · Zbl 0581.65005
[28] Wilson, J. R.; Pritsker, A. A.B., Variance reduction in queueing simulation using generalized concomitant variables, J. Statist. Comput. Simulation, 19, 129-153 (1984) · Zbl 0549.60094
[29] Wilson, J. R.; Pritsker, A. A.B., Experimental evaluation of variance reduction techniques for queueing simulation using generalized concomitant variables, Management Sci., 30, 1459-1472 (1984) · Zbl 0549.60094
[30] Wiriadinata, F., Efficient central-server simulation, (Master’s Thesis (1992), School of Industrial Engineering, Purdue University)
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