Heavy-tailed Dependent Queues in Heavy Traffic

  title={Heavy-tailed Dependent Queues in Heavy Traffic},
  • Published 2008
The paper studies G/G/l queues with heavy-tailed probability distributions of the service times and/or the interarrival times. It relies on the fact that the heavy traffic limiting distribution of the normalized stationary waiting times for such queues is equal to the distribution of the supremum M = supos,, , (x(L)-pt), where X is a LBvy process. This distribution turns out to be exponential if the tail of the distribution of interarrival times is heavier than that of the service times, and it… CONTINUE READING

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Publications referenced by this paper.
Showing 1-10 of 10 references

Convergence of Probability Measures

  • P. Bil l ingsle y
  • 1968
Highly Influential
9 Excerpts

z c z o t k a and W. A. Woyczy riski, Distributions o j suprema of G u y processes via the Heavy R@c Invariance Principle

  • W S
  • Probab. Math. Statist
  • 2003

Szczo t ka, Exponential approximation of waiting time and queue size for queues in heavy trafic

  • I W.
  • Adv. in Appl. Probab
  • 1990

k u bows ki, Principle of conditioning in limit theorems for mms of random variables

  • A. Ja
  • Ann. Probab
  • 1986

Exponential approximation of waiting time and queue size for queues in heavy trafic

  • Szczo t ka
  • Comparison Methods for Queues and Other…
  • 1983

Functional limit theorems for dependent variables

  • R D
  • Ann. Probab
  • 1978

Fluctuation theory in continuous time, Adv

  • N. H. Bingham
  • in Appl. Probab
  • 1975
1 Excerpt

Pet rov

  • V V.
  • Sums of Independent Random Variables,
  • 1975

Ios i fescu and R. T h e o d o r e s cu

  • S M.
  • Random Processes and Learning,
  • 1969

K i n g m a n , The single server queue in heavy traffic

  • J II
  • Proc. Cambridge Philos. Soc
  • 1961

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