Abstract
This study characterizes the behavior of large queue lengths in heavy traffic. We show that the distribution of the maximum queue length in a random time interval for a queueing systems in heavy traffic converges to a novel extreme value distribution. We also study the processes that record the times that the queue length exceeds a high level and the cumulative time the queue is above the level. We show that these processes converge in distribution to compound Poisson processes.
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Chang, KH. Extreme and high-level sojourns of the single server queue in heavy traffic. Queueing Systems 27, 17–35 (1997). https://doi.org/10.1023/A:1019197627948
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DOI: https://doi.org/10.1023/A:1019197627948