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Sensitivity analysis of regenerative queuing models. (English) Zbl 0836.60102

Discrete event dynamical systems may be considered as a different view of using supplemented variables in standard queueing models. For applications these discrete event dynamical systems are models for discrete event simulation programs, e.g., of reliability of queueing systems. Instead of elaborating system properties by focussing on an underlying Markov structure of the processes describing their time evolution the authors evaluate the systems as regenerative processes driven by asynchronous sequences of events. This makes it possible to derive for sensitivity evaluation of performance measures in simulations mathematically rigorous statistical procedures. The aim is to derive sensitivity coefficients defined as (partial) derivatives (of higher order) of desired stationary characteristics of the systems (mean waiting times, loss probabilities, \(\dots\)) with respect to parameters of the distributions of the driving sequences. The approach via regenerative processes allows to weaken assumptions (i.i.d. sequences as driving processes) put on the system before.
Reviewer: H.Daduna (Hamburg)

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
60J05 Discrete-time Markov processes on general state spaces
60K15 Markov renewal processes, semi-Markov processes
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[1] S. Asmussen,Applied Probability and Queues (Wiley, Chichester, 1987).
[2] S. Asmussen and B. Melamed, Regenerative simulation of TES processes, Acta Appl. Math. 34 (1994) 237-260. · Zbl 0804.65146 · doi:10.1007/BF00994268
[3] S. Asmussen and R.Y. Rubinstein, The efficiency and heavy traffic properties of the score function method in sensitivity analysis of queuing models, Adv. Appl. Prob. 24 (1992) 172-201. · Zbl 0745.65088 · doi:10.2307/1427735
[4] S. Asmussen and R.Y. Rubinstein, The performance of likelihood ratio estimators using the score function, Studies in statistical quality control and reliability, Preprint of Chalmers University of Technology, 1 (1990).
[5] N.P. Buslenko, V.V. Kalashnikov and I.N. Kovalenko,Lectures on Complex Systems Theory (Sov. Radio, Moscow, 1973), in Russian.
[6] D. Cox, The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables, Proc. Cambridge Phil. Soc. 51 (1955) 433-441. · Zbl 0067.10902 · doi:10.1017/S0305004100030437
[7] P. Glynn, Likelihood ratio gradient estimation: An overview,Proc. 1989 Winter Simulation Conf., eds. A. Thesen, H. Grant and W.D. Kelton (1989) pp. 366-374.
[8] P. Glynn, Some topics in regenerative steady state simulation, Acta Appl. Math. 34 (1994) 225-236. · Zbl 0799.60084 · doi:10.1007/BF00994267
[9] Gnedenko and I.N. Kovalenko,An Introduction to Queueing Theory (Israel Program for Scientific Translations, Jerusalem, 1968). · Zbl 0186.24502
[10] D. Iglehart and D. Shedler,Regenerative Simulation of Response Times in Networks of Queues (Springer,Verlag, Berlin, 1980). · Zbl 0424.90016
[11] V.V. Kalashnikov,Topics on Regenerative Processes (CRC Press, 1994). · Zbl 0872.60063
[12] V.V. Kalashnikov,Mathematical Methods in Queuing Theory (Kluwer Acad. Publ., Dordrecht, 1994). · Zbl 0836.60098
[13] V.V. Kalashnikov, A.I. Morozov, V.M. Sedunov and L.E. Shashkov, EXAM: An object-oriented environment for simulation experiments, Pattern Recogn. and Image Anal. 2 (1992) 66-76.
[14] M.I. Reiman and A. Weiss, Sensitivity analysis for simulations via likelihood ratios, Oper. Res. 37 (1989) 830-844. · Zbl 0679.62087 · doi:10.1287/opre.37.5.830
[15] R.Y. Rubinstein, Sensitivity analysis and performance extrapolation for computer simulation models, Oper. Res. 37 (1989) 72-81. · doi:10.1287/opre.37.1.72
[16] R.Y. Rubinstein, Decomposable score function estimators for sensitivity analysis and optimization of queueing networks, Ann. Oper. Res. 39 (1992) 195-228. · Zbl 0764.62069 · doi:10.1007/BF02060942
[17] R.Y. Rubinstein and A. Shapiro,Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization via the Score Function Method (Wiley, 1993). · Zbl 0805.93002
[18] D. Shedler,Regeneration and Networks of Queues (Springer, New York, 1987). · Zbl 0607.60083
[19] H. Thorisson, Construction of a stationary regenerative process, Stoch. Proc. Appl. 42 (1992) 237-253. · Zbl 0765.60024 · doi:10.1016/0304-4149(92)90037-Q
[20] B.P. Zeigler, System theoretic foundations of modelling and simulation, NATO ASI Series, Series F, 10 (1984). · Zbl 0589.68070
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