Large deviations for Cox processes and Cox/G/infinity queues, with a biological application

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We show that a sequence of Cox processes on a Polish space E satisfy a large deviation principle (LDP), provided their directing measures do so on the space of finite measures on E equipped with the weak topology. Next, we consider a sequence of infinite server queue with general iid service times, where the arrivals constitute Cox processes with translation invariant directing measures assumed to satisfy an LDP. We show that the corresponding sequence of queue occupancy measures also satisfy an LDP. These questions were motivated by the problem of describing fluctuations of molecule numbers in biochemical reaction networks within cells. Joint work with Justin Dean and Edward Cran.

Ayalvadi Ganesh, University of Bristol

Ayalvadi Ganesh received his BTech in EE from IIT Madras in 1988, MS and PhD in EE from Cornell University in 1991 and 1995 respectively. His Ph.D. thesis was on the use of large deviation techniques in queueing theory. He was with Edinburgh University, Birkbeck College, London, U.K., and Hewlett-Packards Basic Research Institute in Mathematical Sciences (BRIMS) and Microsoft Research before joining the Mathematics Department of Bristol University. He was also a Fellow of Kings College, Cambridge, from 2000 to 2004. He has published extensively on Queueing Theory and Large Deviations, Bayes’ Asymptotics, Economics of Communication Networks, Peer-to-peer Systems and Algorithms, Random graphs and stochastic processes on graphs, and Computer Viruses and Worms. He is the coauthor, with Neil O’Connell and Damon Wischik, of the Springer Book “Big Queues” published in 2004. His research interests are in the mathematical modelling of communication and computer networks, and in decentralised algorithms for such networks. Specific interests include large deviations and applications to queueing theory and statistics, random graph models and stochastic processes on graphs, and decentralised algorithms for resource allocation in the Internet and in wireless networks.