no. 4
An SMDP model for a multiclass multi-server queueing control problem considering conversion times
RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 4, pp. 615-639.

We address a queueing control problem considering service times and conversion times following normal distributions. We formulate the multi-server queueing control problem by constructing a semi-Markov decision process (SMDP) model. The mechanism of state transitions is developed through mathematical derivation of the transition probabilities and transition times. We also study the property of the queueing control system and show that optimizing the objective function of the addressed queueing control problem is equivalent to maximizing the time-average reward.

DOI : 10.1051/ro/2014021
Classification : 60K25, 68M20
Mots clés : queueing control, semi-Markov decision process, reward 
@article{RO_2014__48_4_615_0,
     author = {Zhang, Zhicong and Li, Na and Li, Shuai and Yan, Xiaohui and Guo, Jianwen},
     title = {An {SMDP} model for a multiclass multi-server queueing control problem considering conversion times},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {615--639},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {4},
     year = {2014},
     doi = {10.1051/ro/2014021},
     mrnumber = {3264396},
     language = {en},
     url = {http://www.numdam.org./articles/10.1051/ro/2014021/}
}
TY  - JOUR
AU  - Zhang, Zhicong
AU  - Li, Na
AU  - Li, Shuai
AU  - Yan, Xiaohui
AU  - Guo, Jianwen
TI  - An SMDP model for a multiclass multi-server queueing control problem considering conversion times
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2014
SP  - 615
EP  - 639
VL  - 48
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org./articles/10.1051/ro/2014021/
DO  - 10.1051/ro/2014021
LA  - en
ID  - RO_2014__48_4_615_0
ER  - 
%0 Journal Article
%A Zhang, Zhicong
%A Li, Na
%A Li, Shuai
%A Yan, Xiaohui
%A Guo, Jianwen
%T An SMDP model for a multiclass multi-server queueing control problem considering conversion times
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2014
%P 615-639
%V 48
%N 4
%I EDP-Sciences
%U http://www.numdam.org./articles/10.1051/ro/2014021/
%R 10.1051/ro/2014021
%G en
%F RO_2014__48_4_615_0
Zhang, Zhicong; Li, Na; Li, Shuai; Yan, Xiaohui; Guo, Jianwen. An SMDP model for a multiclass multi-server queueing control problem considering conversion times. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 4, pp. 615-639. doi : 10.1051/ro/2014021. http://www.numdam.org./articles/10.1051/ro/2014021/

[1] R. Andriansyah, T.V. Woensel and F.R.B. Cruz, Performance optimization of open zero-buffer multi-server queueing networks. Comput. Oper. Res. 37 (2010) 1472-1487. | MR | Zbl

[2] A. Azaron, H. Katagiri and K. Kato, Longest path analysis in networks of queues: Dynamic scheduling problems. Eur. J. Oper. Res. 174 (2006) 132-149. | MR | Zbl

[3] S. Borst, N. Hegde and A. Proutière, Interacting queues with server selection and coordinated scheduling-application to cellular data networks. Annal. Oper. Res. 170 (2009) 59-78. | MR | Zbl

[4] C.K. Chen, H.H. Kuo and J.J. Yan, GA-based PID active queue management control design for a class of TCP communication networks. Exp. Syst. Appl. 36 (2009) 1903-1913.

[5] D. Choi, T.S. Kim and S. Lee, Analysis of a queueing system with a general service scheduling function, with applications to telecommunication network traffic control. Eur. J. Oper. Res. 178 (2007) 463-471. | Zbl

[6] A. Choudhury and M. Pallabi, Some aspects of balking and reneging in finite buffer queues. RAIRO-Oper. Res. 45 (2011) 223-240. | Numdam | Zbl

[7] J. Granger, Performance improvement of queueing networks with synchronization stations, Ph.D. dissertation, University of Wisconsin (2006).

[8] M. Harchol-Balter, T. Osogami and A. Scheller-Wolf, Multi-server queueing systems with multiple priority classes. Queueing Syst. 51 (2005) 331-360. | MR | Zbl

[9] M. Haridass and R. Arumuganathan, Analysis of a MX/G (a, b)/1 queueing system with vacation interruption. RAIRO-Oper. Res. 46 (2012) 305-334. | Numdam | MR | Zbl

[10] C. Kim, S. Dudin and V. Klimenok, The MAP/PH/1/N queue with flows of customers as a model for traffic. Perform. Eval. 66 (2009) 564-579.

[11] Y.L. Koçaǧa and A.R. Ward, Admission control for a multi-server queue with abandonment. Queueing Syst. 65 (2010) 275-323. | MR | Zbl

[12] L.B. Le, E. Hossain, A.S. Alfa, Queueing analysis and admission control for multi-rate wireless networks with opportunistic scheduling and ARQ-based error control. IEEE Int. Conf. Commun. 5 (2005) 3329-3333.

[13] Y. Nazarathy and G. Weiss, Near optimal control of queueing networks over a finite time horizon. Annal. Oper. Res. 170 (2009) 233-249. | MR | Zbl

[14] V. Nitto Personè, Analysis of cyclic queueing networks with parallelism and vacation. Annal. Oper. Res. 170 (2009) 95-112. | MR | Zbl

[15] M. Pallabi and A. Choudhury, Aspects of impatience in a finite buffer queue. RAIRO-Oper. Res. 46 (2012) 189-209. | Numdam | MR | Zbl

[16] I.C. Paschalidis, C. Su and M.C. Caramanis, New scheduling policies for multiclass queueing networks: Applications to peer-to-peer systems, in proc. of 42nd IEEE Conf. Decision and Control, Maui, Hawau (2003) 1604-1609.

[17] I.C. Paschalidis, C. Su and M.C. Caramanis, Target-pursuing scheduling and routing policies for multiclass queueing networks. IEEE Trans. Automat. Contr. 49 (2004) 1709-1722. | MR

[18] B. Sikdar and D. Manjunath, Queueing analysis of scheduling policies in copy networks of space-based multicast packet switches. IEEE/ACM Trans. Netw. 8 (2000) 396-406.

[19] P. Tehrani and Q. Zhao, Multichannel scheduling and its connection to queueing network control problem, in proc. of The 2010 Military Communications Conference, San Jose, CA (2010) 482-486.

[20] X. Xu, and Z.G. Zhang, Analysis of multi-server queue with a single vacation (e,d)-policy. Performance Evaluation 63 (2006) 825-838.

Cité par Sources :