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.

Keywords: 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://archive.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://archive.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://archive.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, Volume 48 (2014) no. 4, pp. 615-639. doi : 10.1051/ro/2014021. http://archive.numdam.org/articles/10.1051/ro/2014021/

[1] Performance optimization of open zero-buffer multi-server queueing networks. Comput. Oper. Res. 37 (2010) 1472-1487. | MR | Zbl

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

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

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

, and ,[5] 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

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

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

,[8] Multi-server queueing systems with multiple priority classes. Queueing Syst. 51 (2005) 331-360. | MR | Zbl

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

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

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

and ,[12] 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] Near optimal control of queueing networks over a finite time horizon. Annal. Oper. Res. 170 (2009) 233-249. | MR | Zbl

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

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

and ,[16] 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.

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

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

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

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

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