We consider a Markov decision process for an queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different thresholds. Exact and asymptotic results concerning the computation of the stationary distribution of the model are also derived.
@article{RO_2004__38_2_121_0,
author = {Artalejo, Jesus R. and Economou, Antonis},
title = {Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {121--151},
year = {2004},
publisher = {EDP Sciences},
volume = {38},
number = {2},
doi = {10.1051/ro:2004016},
mrnumber = {2081834},
zbl = {1092.90013},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro:2004016/}
}
TY - JOUR
AU - Artalejo, Jesus R.
AU - Economou, Antonis
TI - Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2004
SP - 121
EP - 151
VL - 38
IS - 2
PB - EDP Sciences
UR - https://www.numdam.org/articles/10.1051/ro:2004016/
DO - 10.1051/ro:2004016
LA - en
ID - RO_2004__38_2_121_0
ER -
%0 Journal Article
%A Artalejo, Jesus R.
%A Economou, Antonis
%T Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2004
%P 121-151
%V 38
%N 2
%I EDP Sciences
%U https://www.numdam.org/articles/10.1051/ro:2004016/
%R 10.1051/ro:2004016
%G en
%F RO_2004__38_2_121_0
Artalejo, Jesus R.; Economou, Antonis. Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers. RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 2, pp. 121-151. doi: 10.1051/ro:2004016
[1] , G-networks: A versatile approach for work removal in queueing networks. Eur. J. Oper. Res. 126 (2000) 233-249. | Zbl | MR
[2] , Dynamic Programming, Deterministic and Stochastic Models. Prentice-Hall, Englewood Cliffs, New Jersey (1987). | Zbl | MR
[3] , Optimal control of bulk queues with compound Poisson arrivals and batch service. Opsearch 21 (1984) 227-245. | Zbl | MR
[4] and, Optimal control of batch service queues. Adv. Appl. Prob. 5 (1973) 340-361. | Zbl | MR
[5] , and, Queueing Networks: Customers, Signals and Product Form Solutions. Wiley, Chichester (1999). | Zbl
[6] , On the control of a compound immigration process through total catastrophes. Eur. J. Oper. Res. 147 (2003) 522-529. | Zbl | MR
[7] and, Computation of the stationary distribution of the queue size in an queueing system with variable service rate. J. Appl. Prob. 17 (1980) 515-522. | Zbl | MR
[8] , Random neural networks with negative and positive signals and product-form solutions. Neural Comput. 1 (1989) 502-510.
[9] , Product-form queueing networks with negative and positive customers. J. Appl. Prob. 28 (1991) 656-663. | Zbl | MR
[10] , G-networks with signals and batch removal. Probab. Eng. Inf. Sci. 7 (1993) 335-342.
[11] , and, Queues with negative arrivals. J. Appl. Prob. 28 (1991) 245-250. | Zbl | MR
[12] and, Stability of product form G-networks. Probab. Eng. Inf. Sci. 6 (1992) 271-276. | Zbl
[13] and, Introduction to Queueing Networks. Wiley, Chichester (1998). | Zbl | MR
[14] and, The M/G/1 queue with negative customers. Adv. Appl. Prob. 28 (1996) 540-566. | Zbl | MR
[15] and, Discrete-time Markov Control Processes. Springer, New York (1996). | Zbl | MR
[16] , Optimal control of a truncated general immigration process through total catastrophes. J. Appl. Prob. 36 (1999) 461-472. | Zbl | MR
[17] , Characterization of the optimal policy for the control of a simple immigration process through total catastrophes. Oper. Res. Letters 24 (1999) 245-248. | Zbl | MR
[18] , and, An system with set-up time for server replacement. Transactions of the Institute of Electronics, Information and Communication Engineers J74-A-10 (1991) 1586-1593.
[19] and, An vacation model with two service modes. Prob. Eng. Inform. Sci. 9 (1994) 355-374. | MR
[20] and, Optimal control of an queue with two service modes. Eur. J. Oper. Res. 113 (1999) 610-619. | Zbl
[21] , Markov Decision Processes. Wiley, New York (1994). | Zbl | MR
[22] , Applied Probability Models with Optimization Applications. Holden-Day Inc., San Francisco (1970). | Zbl | MR
[23] , Introduction to Stochastic Dynamic Programming. Academic Press, New York (1983). | Zbl | MR
[24] , Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley, New York (1999). | Zbl | MR
[25] , and, Mean drifts and the non-ergodicity of Markov chains. Oper. Res. 31 (1983) 783-789. | Zbl | MR
[26] , An equivalence between continuous and discrete time Markov decision processes. Oper. Res. 27 (1979) 616-620. | Zbl | MR
[27] , Comparison Methods for Queues and Other Stochastic Models. Wiley, Chichester (1983). | Zbl | MR
[28] , Control of the service process in a queueing system. Eur. J. Oper. Res. 23 (1986) 141-158. | Zbl | MR
[29] , A First Course in Stochastic Models. Wiley, Chichester (2003). | Zbl | MR
[30] , and, Analysis of M/G/1 stochastic clearing systems. Stochastic Anal. Appl. 20 (2002) 1083-1100. | Zbl | MR
Cité par Sources :
