Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times

This paper considers a stable GI/GI/1 queue with subexponential service time distribution. Under natural assumptions we derive the tail behaviour of the busy period of this queue. We extend the results known for the regular variation case under minimal conditions. Our method of proof is based on a l...

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Bibliographic Details
Published in:Stochastic processes and their applications 2004-06, Vol.111 (2), p.237-258
Main Authors: Baltrūnas, A., Daley, D.J., Klüppelberg, C.
Format: Article
Language:English
Subjects:
1 queue Busy period Subexponential distribution Transient random walk Precise large deviations
Busy period
Exact sciences and technology
GI/GI/1 queue
Limit theorems
Mathematics
Precise large deviations
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Stochastic analysis
Stochastic processes
Subexponential distribution
Transient random walk
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Summary:This paper considers a stable GI/GI/1 queue with subexponential service time distribution. Under natural assumptions we derive the tail behaviour of the busy period of this queue. We extend the results known for the regular variation case under minimal conditions. Our method of proof is based on a large deviations result for subexponential distributions.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2004.01.005