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Convexity properties, moment inequalities and asymptotic exponential approximations for delay distributions in G1/G/1 systems

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  • Delbrouck, L. E. N.

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, [infinity]), 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.

Suggested Citation

  • Delbrouck, L. E. N., 1975. "Convexity properties, moment inequalities and asymptotic exponential approximations for delay distributions in G1/G/1 systems," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 193-207, April.
    • Handle: RePEc:eee:spapps:v:3:y:1975:i:2:p:193-207
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    Cited by:

    1. Heringa, J.R. & Wiegel, F.W. & van Beckum, F.P.H., 1981. "Friction coefficient of a disk in a sheet of viscous fluid: Numerical calculation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 108(2), pages 598-604.

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