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• W2100090121 abstract "Limit theorems are established and relatively simple closed-form approximations are developed for the busy-period distribution in single-server queues. For the M/G/l queue, the complementary busy-period c.d.f. is shown to be asymptotically equivalent as t → ∞ to a scaled version of the heavy-traffic limit (obtained as p → 1), where the scaling parameters are based on the asymptotics as t → ∞. We call this the asymptotic normal approximation, because it involves the standard normal c.d.f. and density. The asymptotic normal approximation is asymptotically correct as t → ∞ for each fixed p and as p → 1 for each fixed t and yields remarkably good approximations for times not too small, whereas the direct heavy-traffic ( p → 1) and asymptotic ( t → ∞) limits do not yield such good approximations. Indeed, even the approximation based on three terms of the standard asymptotic expansion does not perform well unless t is very large. As a basis for generating corresponding approximations for the busy-period distribution in more general models, we also establish a more general heavy-traffic limit theorem." @default.
• W2100090121 created "2016-06-24" @default.
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• W2100090121 date "1995-10-01" @default.
• W2100090121 modified "2023-09-23" @default.
• W2100090121 title "Limits and Approximations for the Busy-Period Distribution in Single-Server Queues" @default.
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• W2100090121 doi "https://doi.org/10.1017/s0269964800004071" @default.
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