We study the equilibrium joining strategies for customers in an M/M/1 queue with working vacations and vacation interruptions. The service rate switches between a low and a high value depending on system dynamics. The server will take a multiple working vacation when the system is empty, during which a low service rate is provided to the arriving customers if any. Upon completion of the first customer’s service, given that the system is not empty, the working vacation will be terminated which means the server comes back and serves the following customers with a higher service rate. Otherwise, if the system is found empty upon completion of the first service, the server will continue his working vacation. Arriving customers may or may not know the state of the server and/or the number of the customers upon arrival, but they have to decide whether to enter the system or balk based on a linear reward-cost structure. We investigate customer behavior according to different levels of information regarding the system state. The equilibrium strategies for the customers are derived and the stationary behavior of the system under these strategies are analyzed. Finally, the effect of different levels of information on equilibrium thresholds and equilibrium entrance probabilities is illustrated by several numerical examples.
Accepté le :
DOI : 10.1051/ro/2015027
Mots clés : Queueing, working vacation, vacation interruptions, equilibrium strategies, stationary distribution
@article{RO_2016__50_3_451_0,
author = {Li, Kaili and Wang, Jinting and Ren, Yanjia and Chang, Jingwei},
title = {Equilibrium joining strategies in {M/M/1} {Queues} with working vacation and vacation interruptions},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {451--471},
publisher = {EDP-Sciences},
volume = {50},
number = {3},
year = {2016},
doi = {10.1051/ro/2015027},
zbl = {1350.60096},
mrnumber = {3519327},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2015027/}
}
TY - JOUR AU - Li, Kaili AU - Wang, Jinting AU - Ren, Yanjia AU - Chang, Jingwei TI - Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2016 SP - 451 EP - 471 VL - 50 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2015027/ DO - 10.1051/ro/2015027 LA - en ID - RO_2016__50_3_451_0 ER -
%0 Journal Article %A Li, Kaili %A Wang, Jinting %A Ren, Yanjia %A Chang, Jingwei %T Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions %J RAIRO - Operations Research - Recherche Opérationnelle %D 2016 %P 451-471 %V 50 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2015027/ %R 10.1051/ro/2015027 %G en %F RO_2016__50_3_451_0
Li, Kaili; Wang, Jinting; Ren, Yanjia; Chang, Jingwei. Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 3, pp. 451-471. doi : 10.1051/ro/2015027. http://www.numdam.org/articles/10.1051/ro/2015027/
, Analysis of a GI/M/1 queue with multiple working vacations. Oper. Res. Lett. 33 (2005) 201–209. | 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
, M/M/1 retrial queue with working vacations. Acta Inform. 47 (2010) 67–75. | DOI | MR | Zbl
, , Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper. Res. Lett. 36 (2008) 696–699. | DOI | MR | Zbl
, and , Optimal balking strategies in single-server queues with general service and vacation times. Perform. Eval. 68 (2011) 967–982. | DOI
S.N. Elaydi, An Introduction to Difference Equations. Mathematics. Springer, New York (1999). | MR | Zbl
and , Strategic behavior and social optimization in Markovian vacation queues. Oper. Res. 59 (2011) 986–997. | DOI | MR | Zbl
and , 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 and M. Haviv, To queue or not to queue: Equilibrium behavior in queueing systems. Kluwer Academic Publishers, Boston, Dordrecht, London (2003). | 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 , Equilibrium balking behavior in the Geo/Geo/1 queueing system with multiple vacations. Appl. Math. Model. 37 (2013) 3861–3878. | DOI | MR | Zbl
and , M/M/1 queue with working vocations (M/M/1/WV). Perform. Eval. 50 (2002) 41–52. | DOI
S. Stidham Jr., Optimal Design of Queueing Systems. CRC Press, Taylor and Francis, Boca Raton (2009). | MR | Zbl
, , Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacation. Top 22 (2013) 694–715. | DOI | MR | Zbl
, and , Equilibrium threshold strategies in observable queueing systems with setup/closedown times. Central Europ. J. Oper. Res. 18 (2010) 241–268. | DOI | MR | Zbl
, and , Pricing and setup/closedown policies in unobservable queues with strategic customers. 4OR: A Quart. J. Oper. Res. 10 (2012) 287–311. | DOI | MR | Zbl
H. Takagi, Queueing Analysis, A Foundation of Performance Evaluation, Vacation and Priority 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
and , Equilibrium analysis of the observable queues with balking and delayed repairs. Appl. Math. Comput. 218 (2011) 2716–2729. | DOI | MR | Zbl
and , M/G/1 queue with multiple working vacations. Perform. Eval. 63 (2006) 654–681. | DOI
, and , Equilibrium balking strategies in Markovian queues with working vacations. Appl. Math. Model. 37 (2013) 8264–8282. | DOI | MR | Zbl
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