Fluid queue driven by a multi-server queue with multiple vacations and vacation interruption
Yu, Senlin1 ; Liu, Zaiming1 ; Wu, Jinbiao1
1 School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. China.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 931-944.

This paper studies a fluid queue driven by a multi-server queue with multiple working vacations and vacation interruption. The stationary distribution of the background environment is obtained after some manipulation. A system of differential equations satisfied by the fluid queue is presented, by which we gain the matrix-geometric structure of the Laplace transform of the stationary buffer content. Furthermore, we derive the explicit expression of the mean buffer content. Finally, the numerical example is employed to illustrate our results.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017002
Classification : 60K25, 68M20
Mots-clés : M/M/c queue, fluid queue, working vacations, buffer content, vacation interruption
Yu, Senlin 1 ; Liu, Zaiming 1 ; Wu, Jinbiao 1

1 School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. China. 
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     title = {Fluid queue driven by a multi-server queue with multiple vacations and vacation interruption},
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     pages = {931--944},
     publisher = {EDP-Sciences},
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Yu, Senlin; Liu, Zaiming; Wu, Jinbiao. Fluid queue driven by a multi-server queue with multiple vacations and vacation interruption. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 931-944. doi : 10.1051/ro/2017002. http://archive.numdam.org/articles/10.1051/ro/2017002/

V. Aggarwal, N. Gautam, S.R.T. Kumara and M. Greaves, Stochastic fluid flow models for determining optimal switching thresholds. Perform. Eval. 59 (2005) 19–46. | DOI

S.I. Ammar, Fluid queue driven by an M/M/1 disasters queue. Int. J. Comput. Math. 91 (2014) 1497–1506. | DOI | MR | Zbl

S.I. Ammar, Analysis of an M/M/1 driven fluid queue with multiple exponential vacations. Appl. Math. Comput. 227 (2014) 329–334. | MR | Zbl

J.W. Baek, H.W. Lee, S.W. Lee and S. Ahn, A MAP-modulated fluid flow model with multiple vacations. Ann. Oper. Res. 202 (2013) 19–34. | DOI | MR | Zbl

J.W. Bosman and R. Numez-Queija, A spectral theory approach for extreme value analysis in a tandem of fluid queues. Queueing Syst. 78 (2014) 121–154. | DOI | MR | Zbl

A. Economou and A. Manou, Strategic behavior in an observable fluid queue with an alternating service process. Eur. J. Oper. Res. 254 (2016) 148–160. | DOI | MR | Zbl

K. Li, J. Wang and Y. Ren, Equilibrium joining strategies in M/M/1 queues with working vacation and vacation interruptions. RAIRO-Oper. Res. 50 (2016) 451–471. | DOI | Numdam | MR | Zbl

Q. Li and Y. Zhao, Block-structured fluid queues driven by QBD processes. Stoch. Anal. Appl. 23 (2005) 1087–1112. | DOI | MR | Zbl

B. Mao, F. Wang and N. Tian, Fluid model driven by an M/G/1 queue with multiple exponential vacations. Appl. Math. Comput. 218 (2011) 4041–4048. | MR | Zbl

D. Mitra, Stochastic theory of a fluid model of producers and consumers coupled by a buffer. Adv. Appl. Probab. 20 (1988) 646–676. | DOI | MR | Zbl

L. Rozovsky, Remarks on a link between the Laplace transform and distribution function of a non-negative random variable. Stat. Probabil. Lett. 79 (2009) 1501–1508. | DOI | MR | Zbl

J. Virtamo and I. Norros, Fluid queue driven by an M/M/1 queue. Queueing Syst. 16 (1994) 373–386. | DOI | MR | Zbl

X. Xu, H. Guo, Y. Zhao and J. Geng, The fluid model driven by the M/M/1 queue with working vacations and vacation interruption. J. Comput. Inf. Syst. 18 (2012) 4041–4048. | Zbl

K. Yan and V.G. Kularni, Optimal inventory policies under stochastic production and demand rates. Stoch. Models 24 (2008) 173–190. | DOI | MR | Zbl

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