Estimating Original Flow Length from Sampled Flow Statistics

In this paper, we consider the problem of non-parametric estimation of network flow characteristics, namely packet lengths and byte sizes, based on sampled flow data. We propose two different approaches to deal with the problem at hand. The first one is based on single stage Bernoulli sampling of packets and their corresponding byte sizes. Subsequently, the flow length distribution is estimated by an adaptive expectation- maximization (EM) algorithm that in addition provides an estimate for the number of active flows. The estimation of the flow sizes (in bytes) is accomplished through a random effects regression model that utilizes the flow length information previously obtained. A variation of this approach, particularly suited for mixture distributions that appear in real network traces, is also considered. The second approach relies on a two-stage sampling procedure, which in the first stage samples flows amongst the active ones, while in the second stage samples packets from the sampled flows. Subsequently, the flow length distribution is estimated using another EM algorithm and the flow byte sizes based on a regression model. The proposed approaches are illustrated and compared on a number of synthetic and real data sets.

This paper compares the sensitivity of aggregate operational Value-at-Risk in the Pareto distribution with that in the Weibull distribution to select an optimal model from the loss severity distributions of approximate goodness-of-fit. After the aggregate operational Value-at-Risk is obtained, the sensitivities of aggregate operational Value-at-Risk are compared when the loss severity distribution are respectively the Pareto and Weibull. The sensitivity of aggregate operational Value-at-Risk with the Pareto distribution is far better than that with the Weibull distribution. Accordingly, the sensitivity of supervised system of operational risk with the Pareto distribution is far better than that with the Weibull distribution. And the Pareto distribution is the optimal model of loss severity distributions. This paper not only finds a new approach to select an optimal model from the distributions of approximate goodness-of-fit, but also connects the selection of distributions with the management of operational risk. This research improves the application of loss distribution approach to the measurement of operational risk.

A Pareto distribution has the property that any tail of the distribution has the same shape as the original distribution. The exponential distribution and the uniform distribution have the tail property too. The tail property characterizes the univariate generalized Pareto distributions. There are three classes of univariate GPDs: Pareto distributions, power laws, and the exponential distribution. All these distributions extend to infinite measures. The tail property translates into a group of symmetries for these infinite measures: translations for the exponential law; multiplications for the Pareto and power laws. In the multivariate case, for cylinder symmetric measures in dimension d >_ 3, there are seven classes of measures with the tail property, corresponding to five symmetry groups. The second part of this paper establishes this classification. The first part introduces the probabilistic setting, and discusses the associated geometric theory of multiparameter regular variation. We prove a remarkable result about a class of multiparameter slowly varying functions introduced in Ostrogorski [1995].

Probability distribution model can affect the extreme value of standard ice thickness on conductors of transmission lines for different return periods. This paper discusses the impact of three probability distribution models on calculation of standard ice thickness, which are Pearson III distribution model (P-III), generalized extreme value distribution model (GEV), and generalized Pareto distribution model (GPD), respectively. The historic icing data have been collected in Lvcongpo Mountain from Hubei province, including icing data from north-south direction, west-east direction, bigger data from two directions, and smaller data from two directions. The analyzing results indicate that GPD is more suitable than P-III and GEV for the icing data collected from Lvcongpo Mountain, which is helpful to reasonably determine the design ice thickness of conductors of transmission lines.

The desire to conceptualize network traffic in a prevailing communication network is a facet for many types of network research studies. In this research, real traffic traces collected over trans-Pacific backbone links (the MAWI repository, providing publicly available anonymized traces) are analyzed to study the underlying traffic patterns. All data analysis and visualization is carried out using Matlab (Matlab is a trademark of The Mathworks, Inc.). At packet level, we first measure parameters such as distribution of packet lengths, distribution of protocol types, and then fit following analytical models. Next, the concept of flow is introduced and flow based analysis is studied. We consider flow related parameters such as top ports seen, duration of the flow, distribution of flow lengths, and number of flows with different timeout values and provide analytical models to fit the flow lengths. Further, we study the amount of data flowing between source-destination pairs. Finally, we focus on TCP-specific aspects of captured traces such as retransmissions and packet round-trip times. From the results obtained, we infer the Zipf-type nature of distribution for number of flows, heavy-tailness of flow sizes and the contribution of well-known ports at packet and flow level. Our study helps a network analyst to farther the knowledge and helps optimize the network resources, while performing efficient traffic engineering.

This work focuses on the study of mechanical and structural properties of glass fiber‐reinforced polypropylene (PPGF) composites compatiblized with maleic anhydride (MAH) grafted PP (PP‐g‐MAH). Thus, effects of the compatibilizer on the flow capacity, fiber orientation and length distribution, thermal and mechanical properties were evaluated. Combining fiber length and melt flow index (MFI) results, it can be speculated that when the compatibilizer is added, the level of fiber matrix interaction increases and the fluidity of the molten composite material improves, resulting in a better orientation and a lower level of fiber length degradation. Moreover, the mechanical analysis based on the micromechanical model was conducted to estimate the effect of the compatibilizer on the interfacial shear stress, orientation factor, and the tensile strength. The main results indicate that the experimental data have confirmed the validity of the micromechanical model. POLYM. COMPOS., 39:3497–3508, 2018. © 2017 Society of Plastics Engineers

This study aims to develop appropriate models for income distribution in Iran using the econophysics approach for the 2006-2018 period. For this purpose, the three improved distributions of the Pareto, Lognormal, and Gibbs-Boltzmann distributions are analyzed with the data extracted from the target household income expansion plan of the statistical centers in Iran. The research results indicate that the income distribution in Iran does not follow the Pareto and Lognormal distributions in most of the study years but follows the generalized Gibbs-Boltzmann distribution function in all study years. According to the results, the generalized Gibbs-Boltzmann distribution also properly fits the actual data distribution and could clearly explain the income distribution in Iran. The generalized Gibbs-Boltzmann distribution also fits the actual income data better than both Pareto and Lognormal distributions.

Software is currently a key part of many safety-critical applications. But the main problem facing the computer industry is how to develop a software with (ultra) high reliability on time, and assure the quality of software. In the past, some researchers reported that the Pareto distribution (PD) and the Weibull distribution (WD) models can be used for software reliability estimation and fault distribution modeling. In this paper we propose a modified PD model to predict and assess the software fault distribution. That is, we suggest using a special form of the Generalized Pareto distribution (GPD) model, named the bounded Generalized Pareto distribution (BGPD) model. We will show that the BGPD model eliminates several modeling issues that arise in the PD model, and perform detailed comparisons based on real software fault data. Experimental result shows that the proposed BGPD model presents very high fitness to the actual fault data. In the end, we conclude that the distribution of faults in a large software system can be well described by the Pareto principle.

To describe the distributions of personal income, many models have been suggested as alternatives to the Pareto distribution. This paper is not intended to review the whole literature about such a subject and to recall the trends which have promoted the research about the above-mentioned models. This kind of work has already been done by C. Dagum (1980) and other authors. Herein it will be pointed out that the type I Pareto distribution has always been an unquestionable reference point and even if such a distribution is not up to describe the left tail of an income distribution, the right tail of an income distribution usually follows the Pareto law. This point of view has been exploited by Dagum (1980) by defining the Pareto weak law. By this author a model of income distribution must obey the Pareto weak law, that is the retrocumulative distribution S(x) must behave like (x/x0)-a when x diverges (a and X0 are conveniently chosen constants).

Selecting series size where the generalized Pareto distribution best fits

Passive traffic measurement increasingly employs sampling at the packet level. Many high-end routers form flow statistics from a sampled substream of packets. Sampling is necessary in order to control the consumption of resources by the measurement operations. However, knowledge of the statistics of flows in the unsampled stream remains useful, for understanding both characteristics of source traffic, and consumption of resources in the network.This paper provide methods that use flow statistics formed from sampled packet stream to infer the absolute frequencies of lengths of flows in the unsampled stream. A key part of our work is inferring the numbers and lengths of flows of original traffic that evaded sampling altogether. We achieve this through statistical inference, and by exploiting protocol level detail reported in flow records. The method has applications to detection and characterization of network attacks: we show how to estimate, from sampled flow statistics, the number of compromised hosts that are sending attack traffic past the measurement point. We also investigate the impact on our results of different implementations of packet sampling.

In recent years, mobile networks have faced with the increase of traffic demand. By emerging mobile applications and cloud computing, Mobile Cloud Computing (MCC) has been introduced. In this research, we focus on the 4th and 5th generation of mobile networks. Data Centers (DCs) are connected to each other by high-speed links in order to minimize delay and energy consumption. By considering a model of the geographical distribution of DCs which uses a wideband optical network, renewable energy and sharing resources for new generations of mobile networks, the real effect of issues on the consumed energy, cost, and profit in the mobile cloud computing are investigated. We derived a penalty function for cost and then by using Lyapunov optimization theorem; we designed an algorithm to minimize the average cost of energy consumption based on the online information in MCC. The time average cost is at most O(1/V) above the optimum target, while the average queue size is O(V). The parameter V can be tuned to make the time average cost as close to (or below) the optimum as desired. We designed three scenarios and two classes of applications to set up our simulation environment. The provided results illustrate the efficiency of our proposed scheme and validate the mathematical model.

Regression testing is a very important part of the program development cycle as it should be executed after feature is integrated or bugs are fixed each time. There are hundreds of test cases in the case library for a little complex product, it is impossible to perform all of the test cases in regression testing every time. Test engineers always select the regression cases by their experience only, most of the cases are executed for several times but cannot find any issues, and many of the defects are escaped from test engineers because of the existing cases have not been selected to run. Pareto distribution model is introduced to assist test engineers in selecting efficient regression cases those are expected to find most of the defects at the incipient stage of testing according to quantitative efficiency of the test cases. And this model helps test engineers to forecast the progress of fault finding also.

Purpose: the purpose of this paper is to develop software that is able to visualise the operation of an IP telephone network under cyberattacks using the mathematical model proposed in the research paper. The software should provide an in-depth analysis of the impact of attacks on network performance, as well as provide results in an easy to interpret graphical form. Methods: mathematical analysis and counting analysis methods were used to achieve the objectives. The basic mathematical models include equations to calculate impact distribution, restoration time and other network parameters. The programme applies numerical integration and differentiation to calculate the service time distribution. The distribution models include exponential, impulse and gamma distributions. Poisson, Weibull and Pareto distributions were used as distribution functions for random data flow parameters. Results: the software is able to simulate different cyberattack scenarios and their impact on key network metrics, analysing characteristics such as delivery time, packet loss probability and network resilience. The results of the analysis show how different types of impacts and recovery parameters affect network performance, allowing the operator to evaluate the effectiveness of different protection and damage techniques. Practical innovativeness: the results obtained in the course of technological modelling can be used to improve the stability and reliability of telecommunication systems, especially those operating on Supertel equipment. The software provides operators with a tool to analyse network conditions, develop preventive measures and optimise post-impact recovery strategies. It can also be integrated into a decision support system and used to identify cases of unauthorised access.

<abstract><p>Trade is one of the essential features of human intelligence. The securities market is the ultimate expression of it. The fundamental indicators of stocks include information about the effects of noise and bias on stock prices; however, distinguishing between them is generally hard. In this article, I present the fundamentals hypothesis based on rational expectations and detect the global bias components from the actual fundamental indicators using a log-normal distribution model based on the fundamentals hypothesis. The analysis results show that biases generally exhibit the same characteristics, strongly supporting our theory. Notably, the positive price-to-cash flows from the investing activities ratio are proxies for the fundamentals. The answer is simple: "Cash is a fact, and profit is an opinion." Namely, opinions of management and accounting added noise to fundamentals. As a result, we obtain the Kesten process and the Pareto distribution. This result means the market knows this noise and shows a stable global bias in the stock market.</p></abstract>