Sharp Bounds on Laplace-Stieltjes Transforms, with Applications to Various Queueing Problems

Eckberg, A.E.

doi:10.1287/moor.2.2.135

Cited by 63 publications

(35 citation statements)

References 13 publications

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“…This occurs because of negative bias in the sample coefficient of variation 2. (Our numerical experience has shown the intuitive result that for a fixed interarrival-time mean, the value of L^ corresponding to a balanced-hyperexponential interarrival time decreases with decreasing coefficient of variation c.) Notice that as sample size increases, the decreasing bias in 2 is reflected in a corresponding decrease in h (2). Perusal of 6(2) in Table V for the other cases reveals that 2 is consistently negatively biased, though the bias always decreases with increasing sample size.…”

Section: Two-moment Behaviourmentioning

confidence: 81%

Behaviour of queueing approximations based on sample moments

Johnson

Luhman

1994

Appl. Stochastic Models Data Anal.

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SUMMARYWe investigate moment-based queueing approximations in the presence of sampling error. Let L be the steady-state mean number in the system for a GI/M/I queue. We focus on the estimation of L under the assumption that only sample moments of the interarrival-time distribution are known. A simulation experiment is carried out for several interarrival-time distributions. For each case, sample moments from the interarrival-time disiribution are matched to a n approximating phase-type distribution and the corresponding estimate_ L is obtained. We show that the sampling error in the moments induces bias as well as variability in L. Based on our simulation experiment, we suggest matching only two moments when the sample coefficient of variation is low or when sample size is low; otherwise, matching three moments is preferable.

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Section: Two-moment Behaviourmentioning

confidence: 81%

Behaviour of queueing approximations based on sample moments

Johnson

Luhman

1994

Appl. Stochastic Models Data Anal.

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“…Closed form solutions for K = 2 and K = 3 are given in Eckberg (1977). For the case K = 2: Figure 1.…”

Section: Resultsmentioning

confidence: 99%

How certain are we about the certainty-equivalent long term social discount rate?

Freeman

Groom

2016

Journal of Environmental Economics and Management

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Theoretical arguments for using a term structure of social discount rates (SDR) that declines with the time horizon have in ‡uenced Government guidelines in the US and Europe. The certainty equivalent discount rate that often underpins this guidance embodies uncertainty in the primitives of the SDR, such as growth.For distant time horizons the probability distributions of these primitives are ambiguous and the certainty equivalent itself is uncertain. Yet, if a limited set of characteristics of the unknown probability distributions can be agreed upon, 'sharp'upper and lower bounds can be de…ned for the certainty-equivalent SDR.Unfortunately, even with considerable agreement on these features, these bounds are widely spread for horizons beyond 75 years. So while estimates of the present value of intergenerational impacts, including the social cost of carbon, can be bounded in the presence of this ambiguity, they typically remain so imprecise as to provide little practical guidance.

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“…That author stands on the works of Holtzman (1973), Eckberg (1977) and Rolski (1972Rolski ( , 1974Rolski ( and 1976) that make similar proposes for parameters and extremal distributions (Note 5).…”

Section: The Peakednessmentioning

confidence: 96%

“…The M to designate the exponential distribution is due to that it fulfills the Memoriless property: For Holtzman (1973) and Eckberg (1983) the peakedness is the ratio of the variance to the mean of the steady-state number of busy servers in a GI/M/∞ system associated to a GI/M/k system. And Eckberg (1977) showed that this parameter, together with the mean, is a much better second parameter than the variance to characterize the inter-arrival time or service time distribution for the GI/M/k system. Then it is recommended in (Whitt, 1984) to use the peakedness instead of the variance.…”

Section: Notesmentioning

confidence: 99%