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.
引用
收藏
页码：199 / 235
页数：37
相关论文
共 50 条
  • [1] A large deviations principle for infinite-server queues in a random environment
    H. M. Jansen
    M. R. H. Mandjes
    K. De Turck
    S. Wittevrongel
    [J]. Queueing Systems, 2016, 82 : 199 - 235
  • [2] A large-deviations analysis of Markov-modulated infinite-server queues
    Blom, J.
    Mandjes, M.
    [J]. OPERATIONS RESEARCH LETTERS, 2013, 41 (03) : 220 - 225
  • [3] INFINITE-SERVER QUEUES WITH HAWKES INPUT
    Koops, D. T.
    Saxena, M.
    Boxma, O. J.
    Mandjes, M.
    [J]. JOURNAL OF APPLIED PROBABILITY, 2018, 55 (03) : 920 - 943
  • [4] A NOTE ON NETWORKS OF INFINITE-SERVER QUEUES
    HARRISON, JM
    LEMOINE, AJ
    [J]. JOURNAL OF APPLIED PROBABILITY, 1981, 18 (02) : 561 - 567
  • [5] Networks of of infinite-server queues with multiplicative transitions
    Fiems, Dieter
    Mandjes, Michel
    Patch, Brendan
    [J]. PERFORMANCE EVALUATION, 2018, 123 : 35 - 49
  • [6] Large deviations of an infinite-server system with a linearly scaled background process
    De Turck, K. E. E. S.
    Mandjes, M. R. H.
    [J]. PERFORMANCE EVALUATION, 2014, 75-76 : 36 - 49
  • [7] Infinite server queues in a random fast oscillatory environment
    Liu, Yiran
    Honnappa, Harsha
    Tindel, Samy
    Yip, Nung Kwan
    [J]. QUEUEING SYSTEMS, 2021, 98 (1-2) : 145 - 179
  • [8] Infinite server queues in a random fast oscillatory environment
    Yiran Liu
    Harsha Honnappa
    Samy Tindel
    Nung Kwan Yip
    [J]. Queueing Systems, 2021, 98 : 145 - 179
  • [9] Tandem of Infinite-Server Queues with Markovian Arrival Process
    Moiseev, Alexander
    Nazarov, Anatoly
    [J]. DISTRIBUTED COMPUTER AND COMMUNICATION NETWORKS, 2016, 601 : 323 - 333
  • [10] Maximum Remaining Service Time in Infinite-Server Queues
    A. V. Lebedev
    [J]. Problems of Information Transmission, 2018, 54 : 176 - 190
12345