Convexity properties,moment inequalities and asymptotic exponential approximations for delay distributions in G1/G/1 systems |
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Authors: | LEN Delbrouck |
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Institution: | Bell-Northern Research, Ottawa, Ontario, Canada |
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Abstract: | Pollaczek distributions pervade the class of delay distibutions in G1/G/1 systems with concave service time distributions. When the service time distribution has finite support and the delay distribution is absolutely continuous on (0, ∞), one can find a distribution with a pure exponential tail that satisfies the corresponding Wiener-Hopf integral equation except for values of the argument that belong to the support in question or to a translate thereof. Again for an exponentially decaying delay distribution, one can formulate sufficient moment inequalities which ensure the existence of asymptotic upper and lower bounds derived from M/D/1 and M/M/1 delay distributions which agree with the former in terms of the first two moments. |
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Keywords: | waiting time Wiener-Hopf equation queueing inequalities compound geometric distribution exponential approximation |
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