Diffusion approximation of an infinite-server queue under Markovian environment with rapid switching

We consider an infinite-server queue with Markov-modulated non-homogeneous arrival and service processes. We adopt the martingale central limit theorem to derive the diffusion approximation of the centered and normalized queue length processes of the queueing system under suitable scaling. In particular, the diffusion approximation results in an Ornstein-Uhlenbeck process with time-varying coefficients and the associated covariance captures the stochastic and predictable variabilities simultaneously.(c) 2023 Elsevier B.V. All rights reserved.