FUNCTIONAL LARGE DEVIATIONS FOR COX PROCESSES AND Cox/G/∞ QUEUES, WITH A BIOLOGICAL APPLICATION
成果类型：
Article
署名作者：
Dean, Justin; Ganesh, Ayalvadi; Crane, Edward
署名单位：
University of Bristol
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/20-AAP1563
发表日期：
2020
页码：
2465-2490
关键词：
摘要：
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.