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

L. E. N. Delbrouck

Stochastic Processes and their Applications, 1975, vol. 3, issue 2, 193-207

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.

Keywords: waiting; time; Wiener-Hopf; equation; queueing; inequalities; compound; geometric; distribution; exponential; approximation (search for similar items in EconPapers)
Date: 1975
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