A heavy-traffic theorem for the G I / G / 1 queue with a Pareto-type service time distribution

J. W. Cohen

International Journal of Stochastic Analysis, 1998, vol. 11, 1-8

Abstract:

For the G I / G / 1 queueing model with traffic load a < 1 , service time distribution B ( t ) and interarrival time distribution A ( t ) , whenever for t → ∞ 1 − B ( t ) ∼ c ( t / β ) ν + O ( e − δ t ) , c > 0 , 1 < ν < 2 , δ > 0 , and ∫ 0 ∞ t μ d A ( t ) < ∞ for μ > ν , ( 1 − a ) 1 ν − 1 w converges in distribution for a ↑ 1 . Here w is distributed as the stationary waiting time distribution. The L.-S. transform of the limiting distribution is derived and an asymptotic series for its tail probabilities is obtained. The theorem actually proved in the text concerns a slightly more general asymptotic behavior of 1 − B ( t ) , t → ∞ , than mentioned above.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:149413

DOI: 10.1155/S1048953398000215

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