A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$queueing model, having time-varying arrival rate and staffing, a generalarrival process satisfying a FCLT, exponential service times and customerabandonment according to a general probability distribution. The FCLT providestheoretical support for the approximating deterministic fluid model the authorsanalyzed in a previous paper and a refined Gaussian process approximation,using variance formulas given here. The model is assumed to alternate betweenunderloaded and overloaded intervals, with critical loading only at theisolated switching points. The proof is based on a recursive analysis of thesystem over these successive intervals, drawing heavily on previous results forinfinite-server models. The FCLT requires careful treatment of the initialconditions for each interval.
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