Partially observable queueing systems with controlled service rates under a discounted optimality criterion
Kybernetika, Tome 57 (2021) no. 3, pp. 493-512
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We are concerned with a class of $GI/GI/1$ queueing systems with controlled service rates, in which the waiting times are only observed when they take zero value. Applying a suitable filtering process, we show the existence of optimal control policies under a discounted optimality criterion.
We are concerned with a class of $GI/GI/1$ queueing systems with controlled service rates, in which the waiting times are only observed when they take zero value. Applying a suitable filtering process, we show the existence of optimal control policies under a discounted optimality criterion.
DOI : 10.14736/kyb-2021-3-0493
Classification : 90B22, 90C39
Keywords: queueing models; partially observable systems; discounted criterion; optimal policies
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García, Yofre H.; Diaz-Infante, Saul; Minjárez-Sosa, J. Adolfo. Partially observable queueing systems with controlled service rates under a discounted optimality criterion. Kybernetika, Tome 57 (2021) no. 3, pp. 493-512. doi: 10.14736/kyb-2021-3-0493

[1] Bensoussan, A., Cakanyildirim, M., Sethi, S. P.: Partially observed inventory systems: the case of zero-balance walk. SIAM J. Control Optim. 46 (2007), 176-209. | DOI

[2] Bauerle, N., Rieder, U.: Markov Decision Processes with Applications to Finance. Springer, Berlin 2011.

[3] Bertsekas, D- P., Shreve, S. E.: Stochastic Optimal Control: The Discrete Time Case. Academic Press, New York 1978. | Zbl

[4] Dynkin, E. B., Yushkevich, A. A.: Controlled Markov Processes. Springer-Verlag, New York 1979. | MR

[5] Elliott, R. J., Aggoun, L., Moore, J. B.: Hidden Markov Models: Estimation and Control. Springer-Verlag, New York 1994.

[6] Gordienko, E., Hernandez-Lerma, O.: Average cost Markov control processes with weighted norms: value iteration. Appl. Math. 23 (1995), 219-237. | DOI

[7] Gordienko, E., Minjarez-Sosa, J. A.: Adaptive control for discrete-time Markov processes with unbounded costs: discounted criterion. Kybernetika 34 (1998), 217-234.

[8] Hernandez-Lerma, O.: Adaptive Markov Control Processes. Springer-Verlag, New York 1989.

[9] Hernandez-Lerma, O., Munoz-de-Ozak, M.: Discrete-time Markov control processes with discounted unbounded costs: optimality criteria. Kybernetika 28 (1992), 191-221.

[10] Kitaev, M. Y., Rykov, V. V.: Controlled Queueing Systems. CRC Press, Boca Raton 1995.

[11] Lindley, D. V.: The theory of queues with a single server. Proc. Cambridge Philos Soc. 48 (1952), 277-289. | DOI

[12] Hilgert, N., Minjarez-Sosa, J. A.: Adaptive policies for time-varying stochastic systems under discounted criterion. Math. Methods Oper. Res. 54 (2001), 491-505. | DOI

[13] Minjarez-Sosa, J. A.: Approximation and estimation in Markov control processes under discounted criterion. Kybernetika 40 (2004), 681-690.

[14] Minjarez-Sosa, J. A.: Markov control models with unknown random state-action-dependent discount factors. TOP 23 (2015), 743-772. | DOI

[15] Runggaldier, W. J., Stettner, L.: Approximations of Discrete Time Partially Observed Control Problems. Appl. Math. Monographs CNR 6, Giardini, Pisa 1994.

[16] Sennott, L. I.: Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley, New York 1999. | Zbl

[17] Striebel, C.: Optimal Control of Discrete Time Stochastic Systems. Lecture Notes Econ. Math. Syst. 110, Springer-Verlag, Berlin 1975. | DOI

[18] Yushkevich, A. A.: Reduction of a controlled Markov model with incomplete data to a problem with complete information in the case of Borel state and control spaces. Theory Probab. Appl.21 (1976), 153-158. | DOI

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