Abstract
Models of discrete event dynamic systems (DEDS) include finite state machines [24], Petri nets [35], finitely recursive processes [26], communicating sequential processes [18], queuing models [41] among others. They become increasingly popular due to important applications in manufacturing systems, communication networks, computer systems. We would consider here a system which evolution or sample path consists of the sequence
where zi(x,ω)) ∈ W is the state of the system during the time interval \({t_i}\left( {x,\omega} \right) \le t < {t_{i + 1}}\left( {x,\omega} \right)\), x∈X⊆Rn is the set of control parameters and ω∈Ω is an element of some probability space (Ω, 𝔹, ℙ). Particular rules which govern transitions between states at time moments ti. can be specified in the framework of one of the models mentioned above. For describing the time behavior the generalized semi- Markov processes proved to be useful [47].
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References
F. Archetti, A. Gaivoronski and A. Sciomachen, Sensitivity analysis and optimization of stochastic Petri Nets, Preprint, University of Milano, 1990.
V. M. Aleksandrov, V. I. Sysoyev and V. V. Shemeneva, Stochastic optimization, Eng. Cybern., v. 5, 1968, p. 11–16.
X. R. Cao, Convergence of parameter sensitivity estimates in a stochastic experiment, IEEE Transactions on Automatic Control, v. AC-30, No. 9, 1985, p. 845–853.
M. A. Crane and D. L. Iglehart. Simulating stable stochastic systems. III. Regenerative processes and discrete-event simulations, Oper. Res. vol.23, 1975, p.33–45.
Yu. Ermoliev, Methods of Stochastic Programming, Nauka, Moscow, 1976 (in Russian).
Yu. Ermoliev and A. A. Gaivoronski, Stochastic programming techniques for optimization of discrete event systems, Annals of Operations Research, 1991.
Yu. Ermoliev, Optimization of discrete event systems described by semi-Markov processes, Lecture at the conference “Computationally intensive methods in Simulation and Optimization”, Vienna, August 1990.
Yu. Ermoliev and Wets, R. J.-B. eds. Numerical Techniques for Stochastic Optimization, Springer-Verlag, Berlin, 1988.
A.A. Gaivoronski, Approximation methods of solution of stochastic programming problems,- Kibernetika, 2, 1982 (in Russian, English translation in: Cybernetics, v. 18, No.2).
A.A. Gaivoronski, Interactive Program SQG-PC for Solving Stochastic Programming Problems on IBM PC/XT/AT Compatibles. User Guide. Working Paper WP-88–11, IIASA, Laxenburg, 1988.
A.A. Gaivoronski, Augmented Perturbation Analysis for optimization of discrete event systems, Preprint, Institute of Cybernetics, Kiev, 1990.
P. Glasserman and W. B. Gong. Smoothed perturbation analysis for a class of discreet-event systems. IEEE Trans. on Automatic Control, 35(11): 1218–1230, 1990.
P.W. Glynn, Optimization of stochastic systems, in: Proceedings of 1986 Winter Simulation Conference, 1986.
P.W. Glynn and J.L. Sanders, Monte Carlo Optimization of Stochastic Systems: Two New Approaches. Proc. 1986 ASME Computing in Engineering Conference, (Chicago, IL) 1986.
W.B. Gong and Y. C. Ho, Smoothed (Conditional) Perturbation Analysis of discrete event dynamic systems, IEEE Transactions on Automatic Control, AC-32, 1987, 856–866.
W. B. Gong, C. G. Cassandras and J. Pan, Perturbation analysis of a multiclass queueing system with admission control. IEEE Transactions on Automatic Control, vol.36, No. 6, 1991, p. 707–723.
P. Heidelberger, Xi-Ren Cao, M. A. Zazanis and R. Suri. Convergence properties of Infinitesimal Perturbation Analysis estimates, Management Science, v. 34, No. 11, 1988.
C. A. R. Hoare, Communicating Sequential Processes. Englewood Cliffs, NJ: Prentice-Hall International, 1985.
Y. C. Ho, Performance evaluation and perturbation analysis of discrete event dynamic systems. IEEE Transactions on Automatic Control, vol. AC-32, No. 7, 1987, p. 563–572.
Y. C. Ho and S. Li, Extensions of Infinitesimal Perturbation Analysis, IEEE Transactions on Automatic Control, AC-33, 1988, p. 427–438.
Y.C. Ho, M. A. Eyler and T. T. Chien. A gradient technique for general buffer storage design in a serial production line. Int. J. Prod. Res., v. 17, No.6, 1979, p. 557–580.
Y.C. Ho, (ed.). A selected and annotated bibliography on perturbation analysis, Lecture Notes in Control and Information Sciences, Vol.103, Springer-Verlag, 1987, pp.162–178.
Y.C. Ho, L. Shi, L. Dai and W. Gong. Optimizing discrete event dynamic systems via the gradient surface method, Manuscript, Harward University, 1990.
J. E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages and Computation, Reading, MA: Addison-Wesley, 1979.
J. Q. Hu and Y.-C. Ho. An infinitesimal perturbation analysis algorithm for a multiclass G/G/1 queue. OR Letters, 9:35–44, 1990.
K. Inan and P. Varaiya, “Finitely recursive process models for discrete event systems”, IEEE Transactions on Automatic Control, v. 33, No.7, 1988, p. 626–639.
S.H. Jacobson and Schruben L.W., Techniques for simulation response optimization, Operations Research Letters, Feb. 1989, 1–9.
P. Kall, Stochastic Linear Programming, Springer Verlag, Berlin, 1976.
J. Kiefer and J. Wolfowitz. Stochastic estimation of a maximum of a regression function, Ann. Math. Statist. 23, 1952, 462–466.
H. Kushner, and D.S. Clark. Stochastic Approximation for Constrained and Unconstrained Systems, Appl. Math. 26, Springer, 1978.
K. Marti, Lecture at the Conference “Computationally intensive methods in Simulation and Optimization”, IIASA, Laxenburg, 1990.
D.L. McLeich and S. Rollans. Conditioning for variance reduction in estimating the sensitivity of simulations. To be published in Annals of Operations Research, 1992.
M. S. Meketon, “Optimization in simulation: A survey of recent results”, Proceedings of the 1987 Winter Simulation Conference, A. Thesen, H. Grant, W. David Keiton (eds), pp. 58–61.
R.H. Myers, Response Surface Methodology, Allyn and Bacon, Boston, Massachusetts, 1987.
J.L. Peterson, Petri Net Theory and the Modelling of Systems. Englewood Cliffs, NJ: Prentice Hall, 1981.
G. Ch. Pflug, On line optimization of simulated Markovian processes. Mathematics of OR, 1990.
G. Ch. Pflug, Derivatives of probability measures — concepts and applications to the optimization of stochastic systems, in: Discrete Events Systems: Models and Applications. IIASA Conference, Sopron, Hungary, August 3–7, 1987, P. Varaiya and A. B. Kurzhanski (eds.), Lecture Notes in Control and Information Sciences, Springer Verlag, 1988, p. 162–178.
G.Ch. Pflug, Optimization of simulated discrete event processes, Preprint TR-ISI/Stamcom 87, University of Vienna, 1990.
M.I. Reiman and A. Weiss, Sensitivity analysis via likelihood ratios, in: Proceedings of the 1986 Winter Simulation Conference, 1986, p. 285–289.
R.Y. Rubinstein, The score function approach of sensitivity analysis of computer simulation models. Math. and Computation in Simulation, vol.28, 1986, p. 351–379.
R.Y. Rubinstein, Monte Carlo Optimization, Simulation and Sensitivity Analysis of Queuing Networks. New York, Wiley, 1986.
R.Y. Rubinstein. How to optimize discrete-event systems from a single sample path by the score function method. Annals of Operations Research 27 (1991) 175–212.
R. Suri, Infinitesimal Perturbation Analysis of General Discrete Event Systems, J. Assoc. Comput. Mach., 34, 1987, 686–717
R. Suri, Perturbation Analysis: The State of the Art and Research Issues Explained via the GI/G/1 Queue, Proceedings of the IEEE, v. 77, No. 1, 1989, 114–137.
R. Suri and Y.T. Leung, Single run optimization of a SIMAN model for automatic assembly systems, Proceedings of the 1987 Winter Simulation Conference, A.Thesen, H.Grant, W. D. Keiton (eds.)
R. J.-B. Wets, Stochastic programming: solution techniques and approximation schemes, in: Mathematical Programming: the State of the Art, 1982, eds. A. Bachern, M. Grotschel and B. Korte, Springer Verlag, 1983, p. 566–603.
W. Whitt, Continuity of generalized semi-Markov process, Math. Oper. Research, vol.5, 1980, p. 494–501.
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Gaivoronski, A.A. (1992). Optimization of Stochastic Discrete Event Dynamic Systems: A Survey of Some Recent Results. In: Pflug, G., Dieter, U. (eds) Simulation and Optimization. Lecture Notes in Economics and Mathematical Systems, vol 374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48914-3_3
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