A heavy-traffic theorem for the queue with a Pareto-type service time distribution
For the queueing model with traffic load , service time distribution and interarrival time distribution , whenever for , and , converges in distribution for . Here 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 , , than mentioned above.
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