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• W2103154048 abstract "We consider the asymptotic variance of the departure counting process D ( t ) of the GI/G/1 queue; D ( t ) denotes the number of departures up to time t . We focus on the case where the system load ϱ equals 1, and prove that the asymptotic variance rate satisfies lim t →∞ var D ( t ) / t = λ(1–2/π)( c a 2 + c s 2 ), where λ is the arrival rate, and c a 2 and c s 2 are squared coefficients of variation of the interarrival and service times, respectively. As a consequence, the departures variability has a remarkable singularity in the case in which ϱ equals 1, in line with the BRAVO (balancing reduces asymptotic variance of outputs) effect which was previously encountered in finite-capacity birth-death queues. Under certain technical conditions, our result generalizes to multiserver queues, as well as to queues with more general arrival and service patterns. For the M/M/1 queue, we present an explicit expression of the variance of D ( t ) for any t ." @default.
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• W2103154048 date "2011-03-01" @default.
• W2103154048 modified "2023-09-26" @default.
• W2103154048 title "The asymptotic variance of departures in critically loaded queues" @default.
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• W2103154048 doi "https://doi.org/10.1239/aap/1300198521" @default.
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