How large delays build up in a GI/G/1 quqe
Queueing Systems: Theory and Applications
Bias correction in effective bandwidth estimation
Performance Evaluation
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Tail Asymptotics for Discrete Event Systems
Discrete Event Dynamic Systems
Control Techniques for Complex Networks
Control Techniques for Complex Networks
Resource dimensioning through buffer sampling
IEEE/ACM Transactions on Networking (TON)
On the estimation of buffer overflow probabilities from measurements
IEEE Transactions on Information Theory
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Large deviations for the empirical mean of an $$M/M/1$$ queue
Queueing Systems: Theory and Applications
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It is known that simulation of the mean position of a Reflected Random Walk (RRW) {W"n} exhibits non-standard behavior, even for light-tailed increment distributions with negative drift. The Large Deviation Principle (LDP) holds for deviations below the mean, but for deviations at the usual speed above the mean the rate function is null. This paper takes a deeper look at this phenomenon. Conditional on a large sample mean, a complete sample path LDP analysis is obtained. Let I denote the rate function for the one dimensional increment process. If I is coercive, then given a large simulated mean position, under general conditions our results imply that the most likely asymptotic behavior, @j^*, of the paths n^-^1W"@?"t"n"@? is to be zero apart from on an interval [T"0,T"1]@?[0,1] and to satisfy the functional equation @?I(ddt@j^*(t))=@l^*(T"1-t)whenever@j(t)0. If I is non-coercive, a similar, but slightly more involved, result holds. These results prove, in broad generality, that Monte Carlo estimates of the steady-state mean position of a RRW have a high likelihood of over-estimation. This has serious implications for the performance evaluation of queueing systems by simulation techniques where steady state expected queue-length and waiting time are key performance metrics. The results show that naive estimates of these quantities from simulation are highly likely to be conservative.