Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-11T12:42:36.738Z Has data issue: false hasContentIssue false
  • English
  • Français

An SMDP model for a multiclass multi-server queueing control problem considering conversion times

Published online by Cambridge University Press:  11 July 2014

Zhicong Zhang ,
Na Li ,
Shuai Li ,
Xiaohui Yan  and
Jianwen Guo
Zhicong Zhang
Affiliation:
Department of Industrial Engineering, School of Mechanical Engineering, Dongguan University of Technology, Songshan Lake District, Dongguan 523808, Guangdong Province, China. . stephen1998@gmail.com; yanxh@dgut.edu.cn; lishuai@dgut.edu.cn
Na Li
Affiliation:
Department of Industrial Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China.; na-li03@sjtu.edu.cn
Shuai Li
Affiliation:
Department of Industrial Engineering, School of Mechanical Engineering, Dongguan University of Technology, Songshan Lake District, Dongguan 523808, Guangdong Province, China. . stephen1998@gmail.com; yanxh@dgut.edu.cn; lishuai@dgut.edu.cn
Xiaohui Yan
Affiliation:
Department of Industrial Engineering, School of Mechanical Engineering, Dongguan University of Technology, Songshan Lake District, Dongguan 523808, Guangdong Province, China. . stephen1998@gmail.com; yanxh@dgut.edu.cn; lishuai@dgut.edu.cn
Jianwen Guo
Affiliation:
School of Mechanical Engineering, Dongguan University of Technology, Songshan Lake District, Dongguan 523808, Guangdong Province, P.R. China. ; guojw@dgut.edu.cn
Get access

Abstract

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 controlsemi-Markov decision processreward
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 4 , October 2014 , pp. 615 - 639
Copyright
© EDP Sciences, ROADEF, SMAI 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andriansyah, R., Woensel, T.V. and Cruz, F.R.B., Performance optimization of open zero-buffer multi-server queueing networks. Comput. Oper. Res. 37 (2010) 1472–1487. Google Scholar
Azaron, A., Katagiri, H. and Kato, K., Longest path analysis in networks of queues: Dynamic scheduling problems. Eur. J. Oper. Res. 174 (2006) 132–149. Google Scholar
Borst, S., Hegde, N. and Proutière, A., Interacting queues with server selection and coordinated scheduling-application to cellular data networks. Annal. Oper. Res. 170 (2009) 59–78. Google Scholar
Chen, C.K., Kuo, H.H. and Yan, J.J., GA-based PID active queue management control design for a class of TCP communication networks. Exp. Syst. Appl. 36 (2009) 1903–1913. Google Scholar
Choi, D., Kim, T.S. and Lee, S., 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. Google Scholar
Choudhury, A. and Pallabi, M., Some aspects of balking and reneging in finite buffer queues. RAIRO-Oper. Res. 45 (2011) 223–240. Google Scholar
J. Granger, Performance improvement of queueing networks with synchronization stations, Ph.D. dissertation, University of Wisconsin (2006).
Harchol-Balter, M., Osogami, T. and Scheller-Wolf, A., Multi-server queueing systems with multiple priority classes. Queueing Syst. 51 (2005) 331–360. Google Scholar
Haridass, M. and Arumuganathan, R., Analysis of a MX/G (a, b)/1 queueing system with vacation interruption. RAIRO-Oper. Res. 46 (2012) 305–334. Google Scholar
Kim, C., Dudin, S. and Klimenok, V., The MAP/PH/1/N queue with flows of customers as a model for traffic. Perform. Eval. 66 (2009) 564–579. Google Scholar
Koçaǧa, Y.L. and Ward, A.R., Admission control for a multi-server queue with abandonment. Queueing Syst. 65 (2010) 275–323. Google Scholar
Le, L.B., Hossain, E., Alfa, A.S., 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. Google Scholar
Nazarathy, Y. and Weiss, G., Near optimal control of queueing networks over a finite time horizon. Annal. Oper. Res. 170 (2009) 233–249. Google Scholar
Nitto Personè, V., Analysis of cyclic queueing networks with parallelism and vacation. Annal. Oper. Res. 170 (2009) 95–112. Google Scholar
Pallabi, M. and Choudhury, A., Aspects of impatience in a finite buffer queue. RAIRO-Oper. Res. 46 (2012) 189–209. Google Scholar
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.
Paschalidis, I.C., Su, C. and Caramanis, M.C., Target-pursuing scheduling and routing policies for multiclass queueing networks. IEEE Trans. Automat. Contr. 49 (2004) 1709–1722. Google Scholar
Sikdar, B. and Manjunath, D., Queueing analysis of scheduling policies in copy networks of space-based multicast packet switches. IEEE/ACM Trans. Netw. 8 (2000) 396–406. Google Scholar
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.
Xu, X., and Zhang, Z.G., Analysis of multi-server queue with a single vacation (e,d)-policy. Performance Evaluation 63 (2006) 825–838. Google Scholar