A large deviations principle for infinite-server queues in a random environment

被引：9
|
作者：
Jansen, H. M. [1 ,2 ]
Mandjes, M. R. H.
De Turck, K. [1 ,3 ]
Wittevrongel, S. [2 ]
机构：
[1] Univ Amsterdam, Korteweg de Vries Inst Math, Sci Pk 904, NL-1098 XH Amsterdam, Netherlands
[2] Univ Ghent, TELIN, Sint Pietersnieuwstr 41, B-9000 Ghent, Belgium
[3] Univ Paris Saclay, Lab Signaux & Syst, Ecole Cent Supelec, L2S,CNRS UMR8506, 3 Rue Joliot Curie, F-91190 Gif Sur Yvette, France
来源：
QUEUEING SYSTEMS | 2016年 / 82卷 / 1-2期
关键词：
Infinite-server queue; Random environment; Modulation; Large deviations principle; TRANSCRIPTION;
D O I：
10.1007/s11134-015-9470-x
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements, and the server work rate are modulated by a general cadlag stochastic background process. To prove a large deviations principle, the concept of attainable parameters is introduced. Scaling both the arrival rates and the background process, a large deviations principle for the number of jobs in the system is derived using attainable parameters. Finally, some known results about Markov-modulated infinite-server queues are generalized and new results for several background processes and scalings are established in examples.
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页码：199 / 235
页数：37
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