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Limiting Diffusions for the Conditioned M/G/1 Queue
Douglas P. Kennedy
Journal of Applied Probability
Vol. 11, No. 2 (Jun., 1974), pp. 355-362
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3212756
Page Count: 8
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The virtual waiting time process, W(t), in the M/G/1 queue is investigated under the condition that the initial busy period terminates but has not done so by time n ≥ t. It is demonstrated that, as n→∞, W(t), suitably scaled and normed, converges to the unsigned Brownian excursion process or a modification of that process depending whether ρ ≠ 1 or ρ = 1, where ρ is the traffic intensity.
Journal of Applied Probability © 1974 Applied Probability Trust