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1999 | 26 | 3 | 315-331
Tytuł artykułu

Semi-Markov control models with average costs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper studies semi-Markov control models with Borel state and control spaces, and unbounded cost functions, under the average cost criterion. Conditions are given for (i) the existence of a solution to the average cost optimality equation, and for (ii) the existence of strong optimal control policies. These conditions are illustrated with a semi-Markov replacement model.
Rocznik
Tom
26
Numer
3
Strony
315-331
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-12-10
poprawiono
1999-04-15
Twórcy
  • Departamento de Matemáticas, Universidad de Sonora, Blvd. Transversal y Rosales s/n, 83000 Hermosillo Sonora, México
  • Departamento de Matemáticas, CINVESTAV-IPN, A. postal 14-740, México D.F. 07000, México
Bibliografia
  • [1] R. B. Ash, Real Analysis and Probability, Academic Press, New York, 1972.
  • [2] R. N. Bhattacharya and M. Majumdar, Controlled semi-Markov models under long-run average rewards, J. Statist. Plann. Inference 22 (1989), 223-242.
  • [3] A. Federgruen, A. Hordijk and H. C. Tijms, Denumerable state semi-Markov decision processes with unbounded costs, average cost criterion, Stochastic Process. Appl. 9 (1979), 222-235.
  • [4] A. Federgruen, P. J. Schweitzer and H. C. Tijms, Denumerable undiscounted semi-Markov decision processes with unbounded rewards, Math. Oper. Res. 8 (1983), 298-313.
  • [5] A. Federgruen and H. C. Tijms, The optimality equation in average cost denumerable state semi-Markov decision problems. Recurrence conditions and algorithms, J. Appl. Probab. 15 (1978), 356-373.
  • [6] P. W. Glynn and S. P. Meyn, A Lyapounov bound for solutions of Poisson's equations, Ann. Probab. 24 (1996), 916-931.
  • [7] E. Gordienko and O. Hernández-Lerma, Average cost Markov control processes with weighted norms: existence of canonical policies, Appl. Math. (Warsaw) 23 (1995), 199-218.
  • [8] U. G. Haussmann, On the optimal long-run control of Markov renewal processes, J. Math. Anal. Appl. 36 (1971), 123-140.
  • [9] O. Hernández-Lerma and J. B. Lasserre, Policy iteration for average cost Markov control processes on Borel spaces, Acta Appl. Math. 47 (1997), 125-154.
  • [10] O. Hernández-Lerma and J. B. Lasserre, Further Topics on Discrete-Time Markov Control Processes, Springer, New York, 1999 (in press).
  • [11] M. Kurano, Semi-Markov decision processes and their applications in the replacement models, J. Oper. Res. Soc. Japan 28 (1985), 18-29.
  • [12] S. A. Lippman, Semi-Markov decision processes with unbounded rewards, Management Sci. 19 (1973), 717-731.
  • [13] S. A. Lippman, On dynamic programming with unbounded rewards, ibid. 21 (1975), 1225-1233.
  • [14] S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer, London, 1993.
  • [15] E. Nummelin, General Irreducible Markov Chains and Non-Negative Operators, Cambridge Univ. Press, Cambridge, 1984.
  • [16] M. L. Puterman, Markov Decision Processes. Discrete Stochastic Dynamic Programming, Wiley, New York, 1994.
  • [17] U. Rieder, Measurable selection theorems for optimization problems, Manuscripta Math. 24 (1978), 115-131.
  • [18] S. M. Ross, Applied Probability Models with Optimization Applications, Holden-Day, San Francisco, 1970.
  • [19] S. M. Ross, Average cost semi-Markov decision processes, J. Appl. Probab. 7 (1970), 649-656.
  • [20] M. Schäl, On the second optimality equation for semi-Markov decision models, Math. Oper. Res. 17 (1992), 470-486.
  • [21] P. J. Schweitzer, Iterative solution of the functional equations of undiscounted Markov renewal programming, J. Math. Anal. Appl. 34 (1971), 495-501.
  • [22] L. I. Sennott, Average cost semi-Markov decision processes and the control of queueing systems, Probab. Engrg. Inform. Sci. 3 (1989), 247-272.
  • [23] H. C. Tijms, Stochastic Models: An Algorithmic Approach, Wiley, Chichester, 1994.
  • [24] O. Vega-Amaya, Markov control processes in Borel spaces: undiscounted criteria, doctoral thesis, UAM-Iztapalapa, México, 1998 (in Spanish).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv26i3p315bwm
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