The asymptotic behavior of queueing systems: Large deviations theory and dominant pole approximation

1996 ◽  
Vol 23 (1-4) ◽  
pp. 27-55 ◽  
Author(s):  
Piet Van Mieghem
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Queueing Systems ◽  
Pole Approximation ◽  
Large Deviations Theory ◽  
Dominant Pole ◽  
Dominant Pole Approximation

scholarly journals Large-Deviations Theory and Empirical Estimator Choice

2008 ◽  
Vol 27 (4-6) ◽  
pp. 513-525 ◽  
Author(s):  
Marian Grendár ◽  
George Judge
Keyword(s):  
Large Deviations ◽  
Large Deviations Theory ◽  
Empirical Estimator

scholarly journals Precise Large Deviations for Random Sums of END Random Variables with Dominated Variation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yu Chen ◽  
Zhihui Qu
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Random Sums ◽  
Tail Probabilities ◽  
Precise Large Deviations ◽  
Surplus Process ◽  
End Random Variables ◽  
Renewal Risk

We investigate the precise large deviations for random sums of extended negatively dependent random variables with long and dominatedly varying tails. We find out that the asymptotic behavior of precise large deviations of random sums is insensitive to the extended negative dependence. We apply the results to a generalized dependent compound renewal risk model including premium process and claim process and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.

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