This paper deals with estimating small tail probabilities of thesteady-state waiting time in a GI/GI/1 queue withheavy-tailed (subexponential) service times. The problem ofestimating infinite horizon ruin probabilities in insurancerisk processes with heavy-tailed claims can be transformed into...

This paper deals with estimating small tail probabilities of thesteady-state waiting time in a GI/GI/1 queue withheavy-tailed (subexponential) service times. The problem ofestimating infinite horizon ruin probabilities in insurancerisk processes with heavy-tailed claims can be transformed into...

Consider a finite-state Markov chain where the transition probabilities differ by orders of magnitude. This Markov chain has an "attractor state," i.e., from any state of the Markov chain there exists a sample path of significant probability to the attractor state. There also exists a "rare...

This paper investigates the likelihood ratio method for estimating derivatives of finite-time performance measures in generalized semi-Markov processes (GSMPs). We develop readily verifiable conditions for the applicability of this method. Our conditions mainly place restrictions on the basic...