scholarly journals Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues

2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Mohan L. Chaudhry ◽  
James J. Kim ◽  
Abhijit D. Banik
Keyword(s):  
Characteristic Equation ◽  
Discrete Time ◽  
Queueing Models ◽  
Computationally Efficient ◽  
Arrival Times ◽  
The Past ◽  
Heavy Tailed Distributions ◽  
Queue Lengths ◽  
Heavy Tailed ◽  
Bulk Arrival

A simple solution to determine the distributions of queue-lengths at different observation epochs for the model GIX/Geo/c is presented. In the past, various discrete-time queueing models, particularly the multiserver bulk-arrival queues, have been solved using complicated methods that lead to incomplete results. The purpose of this paper is to use the roots method to solve the model GIX/Geo/c that leads to a result that is analytically elegant and computationally efficient. This method works well even for the case when the inter-batch-arrival times follow heavy-tailed distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue-lengths at different time epochs.

scholarly journals Two symmetric and computationally efficient Gini correlations

2020 ◽  
Vol 8 (1) ◽  
pp. 373-395
Author(s):  
Courtney Vanderford ◽  
Yongli Sang ◽  
Xin Dang
Keyword(s):  
Influence Function ◽  
Random Variables ◽  
Real Data ◽  
Computationally Efficient ◽  
Gini Correlation ◽  
Heavy Tailed Distributions ◽  
Data Application ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

AbstractStandard Gini correlation plays an important role in measuring the dependence between random variables with heavy-tailed distributions. It is based on the covariance between one variable and the rank of the other. Hence for each pair of random variables, there are two Gini correlations and they are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al (2016) proposed a symmetric Gini correlation based on the joint spatial rank function with a computation cost of O(n2) where n is the sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with the computational complexity of O(n log n). The properties of the new symmetric Gini correlations are explored. The influence function approach is utilized to study the robustness and the asymptotic behavior of these correlations. The asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric log-normal distribution. Simulation and real data application are conducted to demonstrate the desirable performance of the two new symmetric Gini correlations.

scholarly journals Large deviations for the empirical measure of heavy-tailed Markov renewal processes

2016 ◽  
Vol 48 (3) ◽  
pp. 648-671 ◽  
Author(s):  
Mauro Mariani ◽  
Lorenzo Zambotti
Keyword(s):  
Large Deviations ◽  
Finite Graph ◽  
Rate Function ◽  
Empirical Measure ◽  
Markov Renewal Process ◽  
Large Deviations Principle ◽  
Arrival Times ◽  
Heavy Tailed Distributions ◽  
Markov Renewal Processes ◽  
Heavy Tailed

Abstract A large deviations principle is established for the joint law of the empirical measure and the flow measure of a Markov renewal process on a finite graph. We do not assume any bound on the arrival times, allowing heavy-tailed distributions. In particular, the rate function is in general degenerate (it has a nontrivial set of zeros) and not strictly convex. These features show a behaviour highly different from what one may guess with a heuristic Donsker‒Varadhan analysis of the problem.

Analytically Simple and Computationally Efficient Solution to Geo/G/1 and Geo/G/1/N Queues Involving Heavy-tailed Distributions for Service Times

2018 ◽  
Vol 70 (1) ◽  
pp. 74-85
Author(s):  
Mohan L. Chaudhry ◽  
Indra ◽  
Vijay Rajan
Keyword(s):  
Computer Science ◽  
Service Time ◽  
Financial Engineering ◽  
Efficient Solution ◽  
Computationally Efficient ◽  
Heavy Tailed Distributions ◽  
Service Times ◽  
Heavy Tailed

The previous studies pertaining to the queues Geo/G/1 and Geo/G/1/N involve light-tailed distributions for service time. However, due to applications of heavy-tailed distributions in computer science and financial engineering, these distributions are used for service time. This article provides a simple and computationally efficient solution to the queues Geo/G/1 and Geo/G/1/N involving heavy-tailed distributions for service times.

Phänologische Trends bei den Waldbäumen in der Schweiz | Phenological trends regarding the forest trees in Switzerland

2005 ◽  
Vol 156 (6) ◽  
pp. 207-210 ◽  
Author(s):  
Claudio Defila
Keyword(s):  
Regional Differences ◽  
Early Growth ◽  
Horse Chestnut ◽  
Forest Trees ◽  
Spring Season ◽  
Arrival Times ◽  
The Past ◽  
Early Arrival ◽  
Southern Side ◽  
The Alps

Numerous publications are devoted to plant phenological trends of all trees, shrubs and herbs. In this work we focus on trees of the forest. We take into account the spring season (leaf and needle development) as well as the autumn (colour turning and shedding of leaves) for larch, spruce and beech, and,owing to the lack of further autumn phases, the horse chestnut. The proportion of significant trends is variable, depending on the phenological phase. The strongest trend to early arrival in spring was measured for needles of the larch for the period between 1951 and 2000 with over 20 days. The leaves of the horse chestnut show the earliest trend to turn colour in autumn. Beech leaves have also changed colour somewhat earlier over the past 50 years. The trend for shedding leaves, on the other hand, is slightly later. Regional differences were examined for the growth of needles in the larch where the weakest trends towards early growth are found in Canton Jura and the strongest on the southern side of the Alps. The warming of the climate strongly influences phenological arrival times. Trees in the forest react to this to in a similar way to other plants that have been observed (other trees, shrubs and herbs).

Probability and Random Processes

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Random Processes ◽  
Distribution Functions ◽  
Basic Logic ◽  
Heavy Tailed Distributions ◽  
Random Components ◽  
Classical Distribution ◽  
Heavy Tailed ◽  
Basic Facts ◽  
Stochastic Events ◽  
Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

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