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

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• 作者：H. M. Jansen ; M. R. H. Mandjes ; K. De Turck ; S. Wittevrongel
• 关键词：Infinite ; server queue ; Random environment ; Modulation ; Large deviations principle ; 60K25 ; 60F10
• 刊名：Queueing Systems
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：82
• 期：1-2
• 页码：199-235
• 全文大小：670 KB
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• 作者单位：H. M. Jansen (1) (2)
  M. R. H. Mandjes (1)
  K. De Turck (3)
  S. Wittevrongel (2)
  
  1. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands
  2. TELIN, Ghent University, Sint-Pietersnieuwstraat 41, 9000, Ghent, Belgium
  3. Laboratoire Signaux et Systèmes (L2S, CNRS UMR8506), École CentraleSupélec, Université Paris Saclay, 3 Rue Joliot Curie, Plateau de Moulon, 91190, Gif-sur-Yvette, France
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Computer Communication Networks
  Probability Theory and Stochastic Processes
  Production and Logistics
  Systems Theory and Control
  
• 出版者：Springer Netherlands
• ISSN：1572-9443

文摘

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 càdlàg 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. Keywords Infinite-server queue Random environment Modulation Large deviations principle