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

H. M. Jansen (), M. R. H. Mandjes (), K. De Turck () and S. Wittevrongel ()
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H. M. Jansen: University of Amsterdam
M. R. H. Mandjes: University of Amsterdam
K. De Turck: École CentraleSupélec, Université Paris Saclay
S. Wittevrongel: Ghent University

Queueing Systems: Theory and Applications, 2016, vol. 82, issue 1, No 11, 199-235

Abstract: Abstract 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; 60K25; 60F10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11134-015-9470-x

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