Extreme and high-level sojourns of the single server queue in heavy traffic

Authors:
Kuo-Hwa Chang
Affiliations:
Department of Industrial Engineering, Chung-Yuan University,
Venue:
Queueing Systems: Theory and Applications
Year:
1997

Citing 3
Cited 1

Fundamentals of queueing theory (2nd ed.).

Fundamentals of queueing theory (2nd ed.).
Extreme values of queue lengths in M/G/1 and GI/M/1 systems

Mathematics of Operations Research
A heavy traffic limit theorem for networks of queues with multiple customer types

Mathematics of Operations Research

On extreme values in open queueing networks

Mathematical and Computer Modelling: An International Journal

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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.