| Title:
|
Partially observable queueing systems with controlled service rates under a discounted optimality criterion (English) |
| Author:
|
García, Yofre H. |
| Author:
|
Diaz-Infante, Saul |
| Author:
|
Minjárez-Sosa, J. Adolfo |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
493-512 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
queueing models |
| Keyword:
|
partially observable systems |
| Keyword:
|
discounted criterion |
| Keyword:
|
optimal policies |
| MSC:
|
90B22 |
| MSC:
|
90C39 |
| idZBL:
|
Zbl 07442521 |
| idMR:
|
MR4299460 |
| DOI:
|
10.14736/kyb-2021-3-0493 |
| . |
| Date available:
|
2021-11-04T12:47:31Z |
| Last updated:
|
2022-02-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149203 |
| . |
| Reference:
|
[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. |
| Reference:
|
[2] Bauerle, N., Rieder, U.: Markov Decision Processes with Applications to Finance..Springer, Berlin 2011. |
| Reference:
|
[3] Bertsekas, D- P., Shreve, S. E.: Stochastic Optimal Control: The Discrete Time Case..Academic Press, New York 1978. Zbl 0633.93001 |
| Reference:
|
[4] Dynkin, E. B., Yushkevich, A. A.: Controlled Markov Processes..Springer-Verlag, New York 1979. MR 0554083 |
| Reference:
|
[5] Elliott, R. J., Aggoun, L., Moore, J. B.: Hidden Markov Models: Estimation and Control..Springer-Verlag, New York 1994. |
| Reference:
|
[6] Gordienko, E., Hernandez-Lerma, O.: Average cost Markov control processes with weighted norms: value iteration..Appl. Math. 23 (1995), 219-237. |
| Reference:
|
[7] Gordienko, E., Minjarez-Sosa, J. A.: Adaptive control for discrete-time Markov processes with unbounded costs: discounted criterion..Kybernetika 34 (1998), 217-234. |
| Reference:
|
[8] Hernandez-Lerma, O.: Adaptive Markov Control Processes..Springer-Verlag, New York 1989. |
| Reference:
|
[9] Hernandez-Lerma, O., Munoz-de-Ozak, M.: Discrete-time Markov control processes with discounted unbounded costs: optimality criteria..Kybernetika 28 (1992), 191-221. |
| Reference:
|
[10] Kitaev, M. Y., Rykov, V. V.: Controlled Queueing Systems..CRC Press, Boca Raton 1995. |
| Reference:
|
[11] Lindley, D. V.: The theory of queues with a single server..Proc. Cambridge Philos Soc. 48 (1952), 277-289. |
| Reference:
|
[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. |
| Reference:
|
[13] Minjarez-Sosa, J. A.: Approximation and estimation in Markov control processes under discounted criterion..Kybernetika 40 (2004), 681-690. |
| Reference:
|
[14] Minjarez-Sosa, J. A.: Markov control models with unknown random state-action-dependent discount factors..TOP 23 (2015), 743-772. |
| Reference:
|
[15] Runggaldier, W. J., Stettner, L.: Approximations of Discrete Time Partially Observed Control Problems..Appl. Math. Monographs CNR 6, Giardini, Pisa 1994. |
| Reference:
|
[16] Sennott, L. I.: Stochastic Dynamic Programming and the Control of Queueing Systems..Wiley, New York 1999. Zbl 0997.93503 |
| Reference:
|
[17] Striebel, C.: Optimal Control of Discrete Time Stochastic Systems..Lecture Notes Econ. Math. Syst. 110, Springer-Verlag, Berlin 1975. 10.1007/978-3-642-45470-7 |
| Reference:
|
[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. |
| . |
