We study customers’ equilibrium behaviour and social optimization in a single-server Markovian queue with impatient customers and variant of multiple working vacations, where the impatience is due to slow service rate. Under the variant of multiple working vacations, the server takes a working vacation as soon as the system gets empty. When an arriving customer joins the vacation system, it activates an impatience timer. If its patience timer expires before it gets service, the customer abandons the system, and never returns. The server is allowed to take at most successive working vacations, if at the end of a working vacation the system remains empty. An arriving customer takes a decision on the basis of available information whether to join or to balk, which unifies wish for the service as well as reluctance to wait. We discuss equilibrium threshold strategies on the basis of linear reward-cost structure in the fully observable and fully unobservable cases. We present numerical results that establish the impact of the information level as well as various parameters on the equilibrium balking strategies and social benefits. The research outputs may be useful for decision makers to convey information to customers in net benefit maximization and for examining the corresponding social optimization problems.
Mots-clés : Equilibrium balking strategies, customer impatience, multiple working vacations, social optimization
@article{RO_2017__51_3_685_0,
author = {Panda, Gopinath and Goswami, Veena and Banik, Abhijit Datta},
title = {Equilibrium behaviour and social optimization in {Markovian} queues with impatient customers and variant of working vacations},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {685--707},
publisher = {EDP-Sciences},
volume = {51},
number = {3},
year = {2017},
doi = {10.1051/ro/2016056},
mrnumber = {3880519},
zbl = {1382.60113},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2016056/}
}
TY - JOUR AU - Panda, Gopinath AU - Goswami, Veena AU - Banik, Abhijit Datta TI - Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 685 EP - 707 VL - 51 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2016056/ DO - 10.1051/ro/2016056 LA - en ID - RO_2017__51_3_685_0 ER -
%0 Journal Article %A Panda, Gopinath %A Goswami, Veena %A Banik, Abhijit Datta %T Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 685-707 %V 51 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2016056/ %R 10.1051/ro/2016056 %G en %F RO_2017__51_3_685_0
Panda, Gopinath; Goswami, Veena; Banik, Abhijit Datta. Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 685-707. doi : 10.1051/ro/2016056. http://www.numdam.org/articles/10.1051/ro/2016056/
and , Analysis of customers’ impatience in queues with server vacations. Queuing Syst. 52 (2006) 261–279. | DOI | MR | Zbl
and , Infinite-server queues with system’s additional tasks and impatient customers. Probab. Engrg. Inform. Sci. 22 (2008) 477–493. | DOI | MR | Zbl
, , , and , Analytical modeling for delay-sensitive video over WLAN. Multimedia IEEE Trans. 14 (2012) 401–414. | DOI
and , Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes. Eur. J. Oper. Res. 218 (2012) 708–715. | DOI | MR | Zbl
and , Equilibrium customer strategies in a single server Markovian queue with setup times. Queueing Syst. 56 (2007) 213–228. | DOI | MR | Zbl
and , Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper. Res. Lett. 36 (2008) 696–699. | DOI | MR | Zbl
, and , Designing a call center with impatient customers. Manuf. Service Oper. Manag. 4 (2002) 208–227. | DOI
and , Strategic behavior and social optimization in Markovian vacation queues. Oper. Res. 59 (2011) 986–997. | DOI | MR | Zbl
and , Equilibrium strategies for queues with impatient customers. Oper. Res. Lett. 17 (1995) 41–45. | DOI | Zbl
R. Hassin and M. Haviv, To queue or not to queue: Equilibrium behavior in queueing systems. Springer (2003). | MR | Zbl
, and , Analysis of finite buffer Markovian queue with balking, reneging and working vacations. Int. J. Strategic Decis. Sci. 4 (2013) 1–24. | DOI
and , Performance analysis of variant working vacation queue with balking and reneging. Int. J. Math. Oper. Res. 6 (2014) 505–521. | DOI | MR | Zbl
, and , Equilibrium threshold strategies in observable queueing systems under single vacation policy. Appl. Math. Model. 36 (2012) 6186–6202. | DOI | MR | Zbl
and , Queuing management in wireless sensor networks for qos measurement. Wirel. Sensor Netw. 4 (2012) 211. | DOI
, Service center trade-offs between customer impatience and power consumption. Perform. Eval. 68 (2011) 1222–1231. | DOI
and , Queues with slow servers and impatient customers. Eur. J. Oper. Res. 201 (2010) 247–258. | DOI | MR | Zbl
and , An inventory system for perishable items with by-products. Math. Methods Oper. Res. 51 (2000) 287–300. | DOI | MR | Zbl
and , Impatient customers in an M/M/1 queue with single and multiple working vacations. Comput. Ind. Eng. 65 (2013) 207–215. | DOI
and , Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations. Top 22 (2014) 694–715. | DOI | MR | Zbl
H. Takagi, Queueing analysis: A Foundation of Performance Evaluation, in vol. 2. North-Holland (1993). | MR
and , Strategic joining in M/M/1 retrial queues. Eur. J. Oper. Res. 230 (2013) 76–87. | DOI | MR | Zbl
, and , Profit analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Comput. Oper. Res. 34 (2007) 835–847. | DOI | Zbl
, Queues with system disasters and impatient customers when system is down. Queueing Syst. 56 (2007) 195–202. | DOI | MR | Zbl
, , and , Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy. J. Ind. Manag. Optim. 10 (2014) 89–112. | DOI | MR | Zbl
, and , Analysis of customers impatience in an M/M/1 queue with working vacations. J. Ind. Manag. Optim. 8 (2012) 895–908. | DOI | MR | Zbl
, and , Optimal performance analysis of an M/M/1/N queue system with balking, reneging and server vacation. Int. J. Pure Appl. Math. 28 (2006) 101–115. | MR | Zbl
, and , Equilibrium balking strategies in Markovian queues with working vacations. Appl. Math. Model. 37 (2013) 8264–8282. | DOI | MR | Zbl
and , Steady state analysis of the GI/M/1/N queue with a variant of multiple working vacations. Comput. Ind. Eng. 61 (2011) 1296–1301. | DOI
Cité par Sources :
