no. 1
Equilibrium balking strategies in the observable Geo/Geo/1 queue with delayed multiple vacations
Gao, Shan1 ; Wang, Jinting2
1 Department of Mathematics and Statistics, Fuyang Normal College, Fuyang, Anhui 236037, P.R. China.
2 Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P.R. China
RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 119-129.

We consider the discrete-time Markovian single-server queue under delayed multiple vacations. Upon arriving, the customers observe the queue length and decide whether to join or balk. We derive equilibrium threshold balking strategies in two cases, according to the information for the server’s state. We also illustrate the equilibrium thresholds and the social benefits for systems via numerical experiments.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2015019
Classification : 60K25, 90B22
Mots clés : Economics of queues, delayed multiple vacations, equilibrium balking strategies, stationary distribution
Gao, Shan 1 ; Wang, Jinting 2

1 Department of Mathematics and Statistics, Fuyang Normal College, Fuyang, Anhui 236037, P.R. China.
2 Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P.R. China 
@article{RO_2016__50_1_119_0,
     author = {Gao, Shan and Wang, Jinting},
     title = {Equilibrium balking strategies in the observable {Geo/Geo/1} queue with delayed multiple vacations},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {119--129},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {1},
     year = {2016},
     doi = {10.1051/ro/2015019},
     zbl = {1335.60170},
     mrnumber = {3460666},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2015019/}
}
TY  - JOUR
AU  - Gao, Shan
AU  - Wang, Jinting
TI  - Equilibrium balking strategies in the observable Geo/Geo/1 queue with delayed multiple vacations
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2016
SP  - 119
EP  - 129
VL  - 50
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2015019/
DO  - 10.1051/ro/2015019
LA  - en
ID  - RO_2016__50_1_119_0
ER  - 
%0 Journal Article
%A Gao, Shan
%A Wang, Jinting
%T Equilibrium balking strategies in the observable Geo/Geo/1 queue with delayed multiple vacations
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2016
%P 119-129
%V 50
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2015019/
%R 10.1051/ro/2015019
%G en
%F RO_2016__50_1_119_0
Gao, Shan; Wang, Jinting. Equilibrium balking strategies in the observable Geo/Geo/1 queue with delayed multiple vacations. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 119-129. doi : 10.1051/ro/2015019. http://www.numdam.org/articles/10.1051/ro/2015019/

O.Z. Aksin, M. Armony and V. Mehrotra, The modern call-center: a multi-disciplinary perspective on operations management research. Prod. Oper. Manag. 16 (2007) 665–688. | DOI

O. Boudali and A. Economou, Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes. Eur. J. Oper. Res. 218 (2012) 708–715. | DOI | MR | Zbl

A. Burnetas and A. Economou, Equilibrium customer strategies in a single server Markovian queue with setup times. Queueing Syst. 56 (2007) 213–228. | DOI | MR | Zbl

A. Economou and S. Kanta, Optimal balking strategies and pricing for the single server Markovian queue with compartmented waiting space. Queueing Syst. 59 (2008) 237–269. | DOI | MR | Zbl

A. Economou and S. Kanta, Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper. Res. Lett. 36 (2008) 696–699. | DOI | MR | Zbl

A. Economou, A. Gomez-Corral and S. Kanta, Optimal balking strategies in single-server queues with general service and vacation times. Perform. Eval. 68 (2011) 967–982. | DOI

N.M. Edelson and D.K. Hildebrand, Congestion tolls for Poisson queuing processes. Econometrica 43 (1975) 81–92. | DOI | MR | Zbl

P. Guo and R. Hassin, Strategic behavior and social optimization in Markovian vacation queues. Oper. Res. 59 (2011) 986–997. | DOI | MR | Zbl

P. Guo and R. Hassin, Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers. Eur. J. Oper. Res. 222 (2012) 278–286. | DOI | MR | Zbl

R. Hassin, Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue. Nav. Res. Logist. 58 (2011) 107−122. | DOI | Zbl

R. Hassin and M. Haviv, To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Kluwer Academic Publishers, Boston (2003). | MR | Zbl

W. Liu, Y. Ma and J. Li, Equilibrium threshold strategies in observable queueing systems under single vacation policy. Appl. Math. Modell. 36 (2012) 6186–6202. | DOI | MR | Zbl

Y. Ma, W. Liu and J. Li, Equilibrium balking behavior in the Geo/Geo/1 queueing system with multiple vacations. Appl. Math. Model. 37 (2013) 3861–3878. | DOI | MR | Zbl

P. Naor, The regulation of queue size by levying tolls. Econometrica 37 (1969) 15–24. | DOI | Zbl

W. Sun, P. Guo and N. Tian, Equilibrium threshold strategies in observable queueing systems with setup/closedown times. Central Eur. J. Oper. Res. 18 (2010) 241–268. | DOI | MR | Zbl

H. Takagi, Queueing Analysis-A Foundation of Performance Evaluation, Vacation and Prioriry Systems. In Vol. 1. North-Holland, Amsterdam (1991). | MR | Zbl

N. Tian and Z.G. Zhang, Vacation Queueing Models: Theory and Applications. Springer, New York (2006). | MR | Zbl

J. Wang and F. Zhang, Equilibrium analysis of the observable queues with balking and delayed repairs. Appl. Math. Comput. 218 (2011) 2716–2729. | DOI | MR | Zbl

F. Zhang, J. Wang and B. Liu, Equilibrium balking strategies in Markovian queues with working vacations. Appl. Math. Model. 37 (2013) 8264–8282. | DOI | MR | Zbl

Cité par Sources :