A Queueing Theoretic Model of a Gene Regulatory Network

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. 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 first study second order statistics of the equilibrium queue length by
making a simplifying assumption on the service time distribution. We then establish a
Large Deviations Principle for this queueing system in the asymptotic regime in which
the arrival process is sped up, while the service process is not scaled.

Date of Award	23 Jan 2019
Original language	English
Awarding Institution	The University of Bristol
Supervisor	Ayalvadi Ganesh (Supervisor)