Simpler proofs of some properties of the fundamental period of the MAP/G/1 queue

1994 ◽  
Vol 31 (1) ◽  
pp. 235-243 ◽  
Author(s):  
David M. Lucantoni ◽  
Marcel F. Neuts

By an argument which involves matching sample paths, some useful equations for the probability distribution of the fundamental period in the MAP/G/1 queue are derived with less calculational effort than in earlier proofs. It is further shown that analogous equations hold for the MAP/SM/1 queueing model. These results are then used to derive explicit formulas for the mean vectors of the number served during and the duration of the fundamental period.

1994 ◽  
Vol 31 (01) ◽  
pp. 235-243 ◽  
Author(s):  
David M. Lucantoni ◽  
Marcel F. Neuts

By an argument which involves matching sample paths, some useful equations for the probability distribution of the fundamental period in theMAP/G/1 queue are derived with less calculational effort than in earlier proofs. It is further shown that analogous equations hold for theMAP/SM/1 queueing model. These results are then used to derive explicit formulas for the mean vectors of the number served during and the duration of the fundamental period.


1992 ◽  
Vol 24 (01) ◽  
pp. 1-19 ◽  
Author(s):  
G. A. Watterson

The paper considers a random sample of r chromosomes, each having n genes subject to intrachromosomal gene conversion, and mutation. The probability distribution and moments for the number of alleles present is investigated, when the number, k, of possible alleles at each locus, is either finite or infinite. Explicit formulas are given for the mean numbers of alleles on r = 1, 2, or 3 chromosomes, which simplify previously known results. For fixed r, in the infinitely-many-alleles case, the mean number increases asymptotically like r θ log (n) as n→∞, where θ is a mutation parameter. But results for large samples remain elusive.


1992 ◽  
Vol 24 (1) ◽  
pp. 1-19 ◽  
Author(s):  
G. A. Watterson

The paper considers a random sample of r chromosomes, each having n genes subject to intrachromosomal gene conversion, and mutation. The probability distribution and moments for the number of alleles present is investigated, when the number, k, of possible alleles at each locus, is either finite or infinite. Explicit formulas are given for the mean numbers of alleles on r = 1, 2, or 3 chromosomes, which simplify previously known results. For fixed r, in the infinitely-many-alleles case, the mean number increases asymptotically like r θ log (n) as n→∞, where θ is a mutation parameter. But results for large samples remain elusive.


2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.


2021 ◽  
Vol 11 (15) ◽  
pp. 7121
Author(s):  
Shouke Li ◽  
Feipeng Xiao ◽  
Yunfeng Zou ◽  
Shouying Li ◽  
Shucheng Yang ◽  
...  

Wind tunnel tests are carried out for the Commonwealth Advisory Aeronautical Research Council (CAARC) high-rise building with a scale of 1:400 in exposure categories D. The distribution law of extreme pressure coefficients under different conditions is studied. Probability distribution fitting is performed on the measured area-averaged extreme pressure coefficients. The general extreme value (GEV) distribution is preferred for probability distribution fitting of extreme pressure coefficients. From the comparison between the area-averaged coefficients and the value from GB50009-2012, it is indicated that the wind load coefficients from GB50009-2012 may be non-conservative for the CAARC building. The area reduction effect on the extreme wind pressure is smaller than that on the mean wind pressure from the code. The recommended formula of the area reduction factor for the extreme pressure coefficient is proposed in this study. It is found that the mean and the coefficient of variation (COV) for the directionality factors are 0.85 and 0.04, respectively, when the orientation of the building is given. If the uniform distribution is given for the building’s orientation, the mean value of the directionality factors is 0.88, which is close to the directionality factor of 0.90 given in the Chinese specifications.


2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Feng Chu ◽  
Lu Wang ◽  
Xin Liu ◽  
Chengbin Chu ◽  
Yang Sui

Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level.


1960 ◽  
Vol 50 (4) ◽  
pp. 537-552
Author(s):  
G. N. Bycroft

ABSTRACT An investigation is made of the effect of changing the stiffness distribution up the height of a linear shear framed structure when subjected to idealized earthquake motions. The mean value of the largest strains arising in successive earthquakes is determined together with the associated probability distribution. It appears that the chances of finding a strain value greater than twice the mean are very small.


Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 113-122 ◽  
Author(s):  
FRANCK PLOURABOUÉ ◽  
STÉPHANE ROUX ◽  
JEAN SCHMITTBUHL ◽  
JEAN-PIERRE VILOTTE

We study the geometry of the contact between two rigid self-affine surfaces. We investigate the mean shape of the surface in the vicinity of the contact point as well as the probability distribution of apertures a as a function of the distance to the contact point. The latter reveals two distinct scaling regimes which are characterized. We show that as the two surfaces are shifted with respect to each other, the contact point on one surface undergoes a “Levy walk”. If u is the relative shift of the surfaces, the distance d between the two contact points (before and after the shift), scales as d ∝ uα where the exponent α is shown to be equal to the roughness exponent of the surfaces.


Author(s):  
Houdayfa Ounis ◽  
Nawel Aries

The present study aims to present a contribution to the wind resource assessment in Algeria using ERA-Interim reanalysis. Firstly, the ERA-Interim reanalysis 10 m wind speed data are considered for the elaboration of the mean annual 10 m wind speed map for a period starting from 01-01-2000 to 31-12-2017. Moreover, the present study intends to highlight the importance of the descriptive statistics other than the mean in wind resource assessment. On the other hand, this study aims also to select the proper probability distribution for the wind resource assessment in Algeria. Therefore, nine probability distributions were considered, namely: Weibull, Gamma, Inverse Gaussian, Log Normal, Gumbel, Generalized Extreme Value (GEV), Nakagami, Generalized Logistic and Pearson III. Furthermore, in combination with the distribution, three parameter estimation methods were considered, namely, Method of Moment, Maximum Likelihood Method and L-Moment Method. The study showed that Algeria has several wind behaviours due to the diversified topographic, geographic and climatic properties. Moreover, the annual mean 10 m wind speed map showed that the wind speed varies from 2.3 to 5.3 m/s, where 73% of the wind speeds are above 3 m/s. The map also showed that the Algerian Sahara is windiest region, while, the northern fringe envelopes the lowest wind speeds. In addition, it has been shown that the study of the mean wind speeds for the evaluation of the wind potential alone is not enough, and other descriptive statistics must be considered. On the other hand, among the nine considered distribution, it appears that the GEV is the most appropriate probability distribution. Whereas, the Weibull distribution showed its performance only in regions with high wind speeds, which, implies that this probability distribution should not be generalized in the study of the wind speed in Algeria.


1990 ◽  
Vol 27 (01) ◽  
pp. 202-207 ◽  
Author(s):  
Joseph Kupka

A relatively simple formula is presented for the probability distribution of the number K of components of a random function. This formula facilitates the (computer) calculation of the factorial moments of K and yields new expressions for the mean and variance of K.


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