Infinite server queues in a random fast oscillatory environment

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