A note on the asymptotic distribution of the traffic-time-average in a GI/G/∞ with bulk arrivals

Abstract

The asymptotic distribution of the traffic average in the case of M/G/∞ with bulk arrivals has been proved in [7] to be normal with mean μ_Cμ_Pμ_F and variance where and are the variances and μ_P and μ_c are the means of the service-time and the batch-size respectively, μ_F being the mean inter-arrival time. We prove in this note that the asymptotic normality holds even in the more general case of a G//G/∞ with bulk arrivals.