Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
Vladimir Kalashnikov: 1942–2001
Queueing Systems: Theory and Applications
A Note on Veraverbeke's Theorem
Queueing Systems: Theory and Applications
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
Tail behavior of conditional sojourn times in Processor-Sharing queues
Queueing Systems: Theory and Applications
On upper bounds for the tail distribution of geometric sums of subexponential random variables
Queueing Systems: Theory and Applications
Computing ruin probability in the classical risk model
Automation and Remote Control
Queueing Systems: Theory and Applications
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Tails of distributions having the form of the geometric convolution are considered. In the case of light-tailed summands, a simple proof of the famous Cramér asymptotic formula is given via the change of probability measure. Some related results are obtained, namely, bounds of the tails of geometric convolutions, expressions for the distribution of the 1st failure time and failure rate in regenerative systems, and others. In the case of heavy-tailed summands, two-sided bounds of the tail of the geometric convolution are given in the cases where the summands have either Pareto or Weibull distributions. The results obtained have the property that the corresponding lower and upper bounds are tailed-equivalent.