  In this paper, we consider a $G_t/G_t/\infty$ infinite server queueing model
in a random environment. More specifically, the arrival rate in our server is
modeled as a highly fluctuating stochastic process, which arguably takes into
account some small time scale variations often observed in practice. We show a
homogenization property for this system, which yields an approximation by a
$M_t/G_t/\infty$ queue with modified parameters. Our limiting results include
the description of the number of active servers, the total accumulated input
and the solution of the storage equation. Hence in the fast oscillatory context
under consideration, we show how the queuing system in a random environment can
be approximated by a more classical Markovian system.
