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October 2020 Functional large deviations for Cox processes and $\mathit{Cox}/G/\infty$ queues, with a biological application
Justin Dean, Ayalvadi Ganesh, Edward Crane
Ann. Appl. Probab. 30(5): 2465-2490 (October 2020). DOI: 10.1214/20-AAP1563


We consider an infinite-server queue into which customers arrive according to a Cox process and have independent service times with a general distribution. We prove a functional large deviations principle for the equilibrium queue length process. The model is motivated by a linear feed-forward gene regulatory network, in which the rate of protein synthesis is modulated by the number of RNA molecules present in a cell. The system can be modelled as a nonstandard tandem of infinite-server queues, in which the number of customers present in a queue modulates the arrival rate into the next queue in the tandem. We establish large deviation principles for this queueing system in the asymptotic regime in which the arrival process is sped up, while the service process is not scaled.


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Justin Dean. Ayalvadi Ganesh. Edward Crane. "Functional large deviations for Cox processes and $\mathit{Cox}/G/\infty$ queues, with a biological application." Ann. Appl. Probab. 30 (5) 2465 - 2490, October 2020.


Received: 1 August 2018; Revised: 1 November 2019; Published: October 2020
First available in Project Euclid: 15 September 2020

MathSciNet: MR4149534
Digital Object Identifier: 10.1214/20-AAP1563

Primary: 60F10 , 60G55 , 60G57 , 60K25

Keywords: chemical reaction networks , infinite-server queues , large deviations , Point processes , Random measures

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.30 • No. 5 • October 2020
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