共查询到20条相似文献,搜索用时 31 毫秒
1.
B.H. Margolius 《Operations Research Letters》2007,35(1):125-138
We derive the periodic family of asymptotic distributions and the periodic moments for number in the queue for the multi-server queue with Poisson arrivals and exponential service for time-varying periodic arrival and departure rates, and time-varying periodic number of servers. The method is a straight-forward application of generating functions. 相似文献
2.
We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This
traffic class includes the standard models: iid, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently
proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates
of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity
of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions
and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feed-forward
networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky
bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky
bucket.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
In queueing theory, most models are based on time-homogeneous arrival processes and service time distributions. However, in communication networks arrival rates and/or the service capacity usually vary periodically in time. In order to reflect this property accurately, one needs to examine periodic rather than homogeneous queues. In the present paper, the periodic BMAP/PH/c queue is analyzed. This queue has a periodic BMAP arrival process, which is defined in this paper, and phase-type service time distributions. As a Markovian queue, it can be analysed like an (inhomogeneous) Markov jump process. The transient distribution is derived by solving the Kolmogorov forward equations. Furthermore, a stability condition in terms of arrival and service rates is proven and for the case of stability, the asymptotic distribution is given explicitly. This turns out to be a periodic family of probability distributions. It is sketched how to analyze the periodic BMAP/M
t
/c queue with periodically varying service rates by the same method. 相似文献
4.
David J. Scott Diethelm W��rtz Christine Dong Thanh Tam Tran 《Computational Statistics》2011,26(3):459-476
In this paper we demonstrate a recursive method for obtaining the moments of the generalized hyperbolic distribution. The
method is readily programmable for numerical evaluation of moments. For low order moments we also give an alternative derivation
of the moments of the generalized hyperbolic distribution. The expressions given for these moments may be used to obtain moments
for special cases such as the hyperbolic and normal inverse Gaussian distributions. Moments for limiting cases such as the
skew hyperbolic t and variance gamma distributions can be found using the same approach. 相似文献
5.
Satoshi Kuriki Yasuhide Numata 《Annals of the Institute of Statistical Mathematics》2010,62(4):645-672
We provide formulas for the moments of the real and complex noncentral Wishart distributions of general degrees. The obtained
formulas for the real and complex cases are described in terms of the undirected and directed graphs, respectively. By considering
degenerate cases, we give explicit formulas for the moments of bivariate chi-square distributions and 2 × 2 Wishart distributions
by enumerating the graphs. Noting that the Laguerre polynomials can be considered to be moments of a noncentral chi-square
distributions formally, we demonstrate a combinatorial interpretation of the coefficients of the Laguerre polynomials. 相似文献
6.
I. Rahimov 《随机分析与应用》2013,31(5):925-940
Abstract We consider a model of age-dependent branching stochastic process that takes into account the incubation period of the life of individuals. We demonstrate that such processes may be treated as a two-type branching process with a periodic mean matrix. In the case when the Malthusian parameter does not exist study of the process requires additional restrictions on the life and incubation time distributions which define so called subexponential family (Athreya, K. 1972. Branching Processes, Springer, New York). We obtain certain new properties of subexponential distributions, in particular, describe a subclass, which is closed with respect to convolution. Using these results we derive asymptotic behavior of the first and second moments and of the probability of nonextinction. We also prove a limit theorem for the process conditioned on nonextinction. 相似文献
7.
Saralees Nadarajah 《Acta Appl Math》2009,106(1):105-123
Long-tailed distributions arise in many areas of the sciences. These distributions, however, suffer from the weakness of not
having finite moments of all orders and this weakness has restricted their use. In this note, we introduce truncated versions
of five of the most commonly known long-tailed distributions—which possess finite moments of all orders and could therefore
be better models. Explicit expressions for the moments are derived for each of the truncated distributions. Several applications
are illustrated using real data. 相似文献
8.
Wolfgang Stadje 《Operations Research Letters》2003,31(1):1-6
We consider a unit with a random lifetime which is replaced at renewal times by a new identical one regardless of whether it has failed before or not. For this random periodic replacement policy, we derive exact formulas for the cycle length, defined as the time between the replacements of two successive failed units, the stationary probability of the current unit to have failed, and the stationary and the transient distributions of the residual lifetime of the current unit. 相似文献
9.
Raymond Kan 《Journal of computational and graphical statistics》2017,26(4):930-934
Recurrence relations for integrals that involve the density of multivariate normal distributions are developed. These recursions allow fast computation of the moments of folded and truncated multivariate normal distributions. Besides being numerically efficient, the proposed recursions also allow us to obtain explicit expressions of low-order moments of folded and truncated multivariate normal distributions. Supplementary material for this article is available online. 相似文献
10.
股票收益率的次指数分布拟合 总被引:4,自引:0,他引:4
股票收益率等金融时间序列具有重尾特征,因而不适于用正态分布来描述,次指数分布族S是一类重尾分布族,能够很好的处理具有偏态、重尾特征的金融时间序列,本文对上证指数的收益率进行了次指数分布拟合,并给出了在险价值(VaR)的估计。 相似文献
11.
《Optimization》2012,61(4):587-599
A method of generating probability distributions of the number of customers served in a busy period of a steady state single-server queueing system with univariate and multivariate inputs is described. A few moments in terms of the moments of the input distributions are derived. Some applications of the busy period distributions to such areas as branching processes, traffic flows, first passage problems, ballot theorems and waiting time distributions are briefly mentioned. 相似文献
12.
We present formulas and recurrence formulas commonly used in insurance mathematics for moments of counting distributions given
by the kth-order recursion. Moreover, we develop recurrence formulas for moments of compound distributions with those counting
distributions satisfying the kth-order recursion.
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part II. 相似文献
13.
For a wide class of discrete distributions, we derive a representation of the inverse (negative) moments through the Stirling numbers of the first kind and inverse factorial moments. We specialize the results for the Poisson, binomial, hypergeometric and negative binomial distributions. 相似文献
14.
Restricted to certain classes of discrete life distributions, and based on moments, conditional binomial moments, order statistics, spacing or record values, characterizations of geometric distributions are given.This project is supported by the National Natural Science Foundation of China Grant No. 1880492. 相似文献
15.
An investigation of phase-distribution moment-matching algorithms for use in queueing models 总被引:1,自引:0,他引:1
Algorithms for matching moments to phase-type distributions are evaluated on the basis of their performance in their intended
application, queueing models. The moment-matching algorithms under consideration match two moments to a hyperexponential distribution
with balanced means and three moments to a mixture of two Erlang distributions of common order. These algorithms are used
to approximate an interarrival-time distribution for a queueing model, and the accuracy of associated performance-measure
approximations is then used to evaluate the moment-matching algorithms. Three performance measures are considered, and attention
is focussed on the steady-state mean queue length (number in system) of theGI/M/1 queue. Performance-measure approximations are compared to three-moment bounds and performance-measure values arising from
hypothetical approximated distributions. 相似文献
16.
After defining generating functions,this paper discusses their properties,and then provides a sufFcient and necessary condition for a finite property of the moments of first entrance time distributions of Markov chains in random environments by generating functions.Finally,the paper obtains relevant conclusions of the moments of first entrance time distributions. 相似文献
17.
The evolution of the state sizes of a closed continuous-time homogeneous Markov system is determined by the convolution of
multinomial distributions expressing the number of transitions between the states of the system. In order to investigate the
distributions of the state sizes, we provide the computation of their moments, at any time point, via a recursive formula
concerning the derivative of the moments. The basic result is given by means of a new vector product which is similar to the
Kronecker product. Finally, a formula for the computation of the state sizes distributions is given. 相似文献
18.
James R. Schott 《Statistics & probability letters》2002,60(4):395-404
Many normal-theory test procedures for covariance matrices remain valid outside the family of normal distributions if the matrix of fourth-order moments has structure similar to that of a normal distribution. In particular, for elliptical distributions this matrix of fourth-order moments is a scalar multiple of that for the normal, and for this reason many normal-theory statistics can be adjusted by a scalar multiple so as to retain their asymptotic distributional properties across elliptical distributions. For these analyses, a test for the validity of these scalar-adjusted normal-theory procedures can be viewed as a test on the structure of the matrix of fourth-order moments. In this paper, we develop a Wald statistic for conducting such a test. 相似文献
19.
K. V. Lykov 《Mathematical Notes》2012,91(1-2):69-80
It is well known that that the coincidence of integer moments (nth-power moments, where n is an integer) of two nonnegative random variables does not imply the coincidence of their distributions. Moreover, we show that, given coinciding integer moments, the ratio of half-integer moments may tend to infinity arbitrarily fast. Also, in this paper, we give a new proof of uniqueness in the continuous moment problem and show that, in that problem, it is impossible to replace the condition of coincidence of all moments by a two-sided inequality between them, while preserving the inequality between the distributions. In conclusion, we study the relationship with the theory of extrapolation of spaces. 相似文献
20.
In this paper a higher order approximation for single server queues and tandem queueing networks is proposed and studied. Different from the most popular two-moment based approximations in the literature, the higher order approximation uses the higher moments of the interarrival and service distributions in evaluating the performance measures for queueing networks. It is built upon the MacLaurin series analysis, a method that is recently developed to analyze single-node queues, along with the idea of decomposition using higher orders of the moments matched to a distribution. The approximation is computationally flexible in that it can use as many moments of the interarrival and service distributions as desired and produce the corresponding moments for the waiting and interdeparture times. Therefore it can also be used to study several interesting issues that arise in the study of queueing network approximations, such as the effects of higher moments and correlations. Numerical results for single server queues and tandem queueing networks show that this approximation is better than the two-moment based approximations in most cases. 相似文献