Stochastic models of gene expression are typically formulated using the
chemical master equation, which can be solved exactly or approximately using a
repertoire of analytical methods. Here, we provide a tutorial review of an
alternative approach based on queuing theory that has rarely been used in the
literature of gene expression. We discuss the interpretation of six types of
infinite server queues from the angle of stochastic single-cell biology and
provide analytical expressions for the stationary and non-stationary
distributions and/or moments of mRNA/protein numbers, and bounds on the Fano
factor. This approach may enable the solution of complex models which have
hitherto evaded analytical solution.Comment: 24 pages, 6 figure