Functional large deviations for Cox processes and Cox/G/∞ queues, with a biological application

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Abstract

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 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.
Original languageEnglish
Pages (from-to)2465-2490
Number of pages26
JournalAnnals of Applied Probability
Volume30
Issue number5
DOIs
Publication statusAccepted/In press - 19 Jan 2020

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