A Novel Double-Time-Scale Evaluation Method for Ethernet Performability

Generally, there are two ways in Ethernet study, i.e., structural reliability analysis and performance evaluation. The former cannot evaluate the ability of Ethernet to perform particular functionalities precisely, whereas the later ignores random failures, and thus cannot reflect the long-term performance degradation of Ethernet. This article proposes a novel double-time-scale evaluation method to overcome the above disadvantages. The study of Ethernet is conducted in Macro and Micro levels, i.e., the relationship between the number of operational workstations and the random failures is formulated in Macro scale, and the performance is modeled with the number of operational workstations in Micro scale. This method can synthesize the effect of reliability and performance, and evaluate the Ethernet in a systematic way effectively. It reflects the actual influence of random failures on Ethernet performance degradation. Because the impact of main Ethernet design parameters is included in the analytical model of Ethernet performability, this method offers a powerful tool for design optimization of the Ethernet.     

The Modelling of Ethernet Data and of Signals that are Heavy‐tailed with Infinite Variance*

We provide an overview of some of the research of the last ten years involving computer network data traffic. We describe the original Ethernet data study which suggested that computer traffic is inherently different from telephone traffic and that in the context of computer networks, self‐similar models such as fractional Brownian motion, should be used. We show that the on–off model can physically explain the presence of self‐similarity. While the on–off model involves bounded signals, it is also possible to consider arbitrary unbounded finite‐variance signals or even infinite‐variance signals whose distributions have heavy tails. We show that, in the latter case, one can still obtain self‐similar processes with dependent increments, but these are not the infinite‐variance fractional stable Lévy motions which have been commonly considered in the literature. The adequate model, in fact, can either have dependent or independent increments, and this depends on the respective size of two parameters, namely, the number of workstations in the network and the time scale under consideration. We indicate what happens when these two parameters become jointly asymptotically large. We conclude with some comments about high frequency behaviour and multifractals.     

Software reliability assessment using accelerated testing methods

The use of operational profiles and usage-based testing has received considerable attention recently in the software engineering literature. Testing under the actual operational profile can, however, be expensive, time consuming or even infeasible in situations where the performance of a system is dominated by infrequent but highly critical events. We consider a real application that deals with telecommunications network restoration after network failure caused by cuts in fibre optic cables. We use this application to demonstrate the usefulness of traditional accelerated testing methods to test and estimate software reliability. These methods, which have been extensively used in hardware reliability, have an important role to play in software reliability assessment as well.     

物流配送网的资源优化配置研究

基于图论中的路径优化理论提出了一种物流配送网层次表达模型,该模型以最小化运输成本为优化目的,采用不同的边和权值表示不同的配送方式,通过调整边的分布和边的权值,再利用改进的Dijkstra路由算法在动态变化的配送网络中为配送请求寻找最优运输路径。通过和其他传统配送方法的仿真比较证明层次表达模型在运输成本和配送业务的损失率上都有更好的性能。     

End-to-end queuing delay assessment in multi-service ip networks

Packet-based networks are more and more used to transport interactive streaming services like telephony and videophony. To guarantee a good quality for these services, the queuing delay and delay jitter introduced in the transport of voice or video flows over the packet-based network should be kept under control. Because data sources tend to increase their sending rate until (a part of) the network is congested, mixing real-time traffic and data traffic in one queue would lead to unacceptable high delays for real-time services. Therefore, voice and video packets need to get preferential treatment ( e.g. head-of-line priority) over data packets in the network nodes. Therefore, the queuing behavior of the voice and video packets can be studied more or less independently from the traffic generated by data services. Simple methods to assess the end-to-end delay are primordial. Since it is well known that an aggregate of voice (and CBR video) sources is accurately modeled by a Poisson arrival process and that delays in consecutive nodes are more or less statistically independent, this boils down to developing methods to calculate quantiles of the total queuing delay through a system of N statistically independent M/G/1 nodes. This paper develops four methods to calculate quantiles of the total queuing delay: a Gaussian method, a method based on the numerical inversion of the moment generating function of the total queuing delay developed by Abate and Whitt and two methods based on the assumption that the tail distribution of the individual queuing delay of one node is approximately exponential. The Gaussian method is the simplest, but only gives crude results. The method of Abate and Whitt is the most complex and breaks down for large quantiles. The methods based on the assumption of an exponential tail produce results that are more or less equally accurate as long as there is a node where the load is high enough.     

On weak convergence of long-range-dependent traffic processes

A possible model for communication traffic is that the amount of work arriving in successive time intervals is jointly Gaussian. This model seems to fly in the face of certain obvious and characteristic features of real traffic, such as the fact that it arrives in discrete bundles and that there is often a non-zero probability of zero traffic in a time interval of significant length. Also, the Gaussian model allows the possibility of negative traffic, which is clearly unrealistic. As the number of sources of traffic increases and the quantity of traffic in communication networks increases, however, under suitable conditions, the deviation between the distribution of real traffic and the Gaussian model will become less. The appropriate concept of topology/convergence must be used or the result will be meaningless. To identify an appropriate convergence framework, the performance statistics associated with a network, namely cell loss, delay, and, in general, statistics which can be expressed in terms of the network buffers which accumulate in the network may be used as a guide. Weak convergence of probability measures has the property that when the probability measures of traffic processes converge to that of a certain traffic process, the distribution of their performance characteristics, such as buffer occupancy, also converges in the same sense to the performance of the system to which they were converging. Real traffic appears, unambiguously, to be long-range dependent. There is an interesting example where aggregation of traffic does not seem to produce convergence to the queueing behaviour expected of Gaussian traffic, at any rate the tail characteristics do not converge to those of the Gaussian result. However, in Section 4, it is shown that if the variance of one traffic stream is finite and as a proportion of the variance of the whole traffic volume tends to zero, then the traffic in networks can be expected to converge to Gaussian in the sense of weak convergence of probability measures. It is then shown that, as a consequence, the traffic in the paradoxical example does converge in this sense also. The paradox is explained by noticing that asymptotic tail behaviour may become increasingly irrelevant as traffic is aggregated. This fact should sound a warning concerning the cavalier use of tail-behaviour as an indication of performance. Long-range dependence apparently places no inhibition on convergence to Gaussian behaviour. Convergence to a Gaussian distribution of increasing aggregates of traffic is only shown to occur for discrete time models. In fact it appears that continuous time Gaussian models do not share this property and their use for modelling real traffic may be problematic.     

Bayesian Time Series Analysis of Structural Changes in Level and Trend

In this article we consider the problem of detecting changes in level and trend in time series model in which the number of change-points is unknown. The approach of Bayesian stochastic search model selection is introduced to detect the configuration of changes in a time series. The number and positions of change-points are determined by a sequence of change-dependent parameters. The sequence is estimated by its posterior distribution via the maximum a posteriori (MAP) estimation. Markov chain Monte Carlo (MCMC) method is used to estimate posterior distributions of parameters. Some actual data examples including a time series of traffic accidents and two hydrological time series are analyzed.     

Economic design of quick switching sampling system for assuring Weibull distributed mean life

In this paper, we propose the quick switching sampling system for assuring mean life of a product under time truncated life test where the lifetime of the product follows the Weibull distribution and the mean life is considered as the quality of the product. The optimal parameters of the proposed system are determined using two points on the operating characteristic curve approach for various combinations of consumer's risk and ratio of true mean life time and specified life time. Tables are constructed to determine the optimal parameters for specified acceptable quality level and limiting quality level along with the corresponding probabilities of acceptance. The proposed system is compared with other existing sampling plans under Weibull lifetime model. In addition, an economical design of the proposed system is also discussed.     

基于Markov区制转换模型的极值风险度量研究

将马尔科夫区制转换模型与极值理论相结合研究金融风险度量问题.首先用SWARCH-t模型捕捉收益率序列的剧烈波动和结构变换特征,然后将收益序列转化为标准残差序列,在此基础上通过SWARCH-t模型与极值理论相结合拟合标准残差的尾部分布,进而构建基于SWARCH- t- EVT的动态VaR模型,最后对模型的有效性进行检验.研究表明,SWARCH-t-EVT模型能够有效识别上证综指的波动区制特征,且能有效合理地测度上证综指收益风险,尤其在高的置信水平下表现更好.     

ELICITING A DIRECTED ACYCLIC GRAPH FOR A MULTIVARIATE TIME SERIES OF VEHICLE COUNTS IN A TRAFFIC NETWORK

The problem of modelling multivariate time series of vehicle counts in traffic networks is considered. It is proposed to use a model called the linear multiregression dynamic model (LMDM). The LMDM is a multivariate Bayesian dynamic model which uses any conditional independence and causal structure across the time series to break down the complex multivariate model into simpler univariate dynamic linear models. The conditional independence and causal structure in the time series can be represented by a directed acyclic graph (DAG). The DAG not only gives a useful pictorial representation of the multivariate structure, but it is also used to build the LMDM. Therefore, eliciting a DAG which gives a realistic representation of the series is a crucial part of the modelling process. A DAG is elicited for the multivariate time series of hourly vehicle counts at the junction of three major roads in the UK. A flow diagram is introduced to give a pictorial representation of the possible vehicle routes through the network. It is shown how this flow diagram, together with a map of the network, can suggest a DAG for the time series suitable for use with an LMDM.     

A class of models for aggregated traffic volume time series

Summary. The development of time series models for traffic volume data constitutes an important step in constructing automated tools for the management of computing infrastructure resources. We analyse two traffic volume time series: one is the volume of hard disc activity, aggregated into half-hour periods, measured on a workstation, and the other is the volume of Internet requests made to a workstation. Both of these time series exhibit features that are typical of network traffic data, namely strong seasonal components and highly non-Gaussian distributions. For these time series, a particular class of non-linear state space models is proposed, and practical techniques for model fitting and forecasting are demonstrated.     

Smoothing Time Series with Local Polynomial Regression on Time

Time series smoothers estimate the level of a time series at time t as its conditional expectation given present, past and future observations, with the smoothed value depending on the estimated time series model. Alternatively, local polynomial regressions on time can be used to estimate the level, with the implied smoothed value depending on the weight function and the bandwidth in the local linear least squares fit. In this article we compare the two smoothing approaches and describe their similarities. Through simulations, we assess the increase in the mean square error that results when approximating the estimated optimal time series smoother with the local regression estimate of the level.     

Residual analysis for parametric models fit to censored data

The focus of this paper is on residual analysis for the lognormal and extreme value or Weibull models, although the proposed methods can be applied to any parametric model. Residuals developed by Barlow and Prentice (1988) for the Cox proportional hazards model are extended to the parametric model setting. Three different residuals are proposed based on this approach with two residuals measuring the impact of survival time and one measuring the impact of the covariates included in the model. In addition, a residual derived from the deviations equality presented in Efron and Johnstone (1990) and the residual proposed by Joergensen (1984) for censored data models are discussed.     

Optimal Design for Step-Stress Accelerated Degradation Test with Multiple Performance Characteristics Based on Gamma Processes

Step-stress accelerated degradation test (SSADT) plays an important role in assessing the lifetime distribution of highly reliable products under normal operating conditions when there are not enough test units available for testing purposes. Recently, the optimal SSADT plans are presented based on an underlying assumption that there is only one performance characteristic. However, many highly reliable products usually have complex structure, with their reliability being evaluated by two or more performance characteristics. At the same time, the degradation of these performance characteristics would be always positive and strictly increasing. In such a case, the gamma process is usually considered as a degradation process due to its independent and nonnegative increments properties. Therefore, it is of great interest to design an efficient SSADT plan for the products with multiple performance characteristics based on gamma processes. In this work, we first introduce reliability model of the degradation products with two performance characteristics based on gamma processes, and then present the corresponding SSADT model. Next, under the constraint of total experimental cost, the optimal settings such as sample size, measurement times, and measurement frequency are obtained by minimizing the asymptotic variance of the estimated 100 qth percentile of the product’s lifetime distribution. Finally, a numerical example is given to illustrate the proposed procedure.     

Two Applications of Statistics to Traffic Models

Two statistical applications for estimation and prediction of flows in traffic networks are presented. In the first, the number of route users are assumed to be independent α-shifted gamma Γ(θ, λ₀) random variables denoted H(α, θ, λ₀), with common λ₀. As a consequence, the link, OD (origin-destination) and node flows are also H(α, θ, λ₀) variables. We assume that the main source of information is plate scanning, which permits us to identify, totally or partially, the vehicle route, OD and link flows by scanning their corresponding plate numbers at an adequately selected subset of links. A Bayesian approach using conjugate families is proposed that allows us to estimate different traffic flows. In the second application, a stochastic demand dynamic traffic model to predict some traffic variables and their time evolution in real networks is presented. The Bayesian network model considers that the variables are generalized Beta variables such that when marginally transformed to standard normal become multivariate normal. The model is able to provide a point estimate, a confidence interval or the density of the variable being predicted. Finally, the models are illustrated by their application to the Nguyen Dupuis network and the Vermont-State example. The resulting traffic predictions seem to be promising for real traffic networks and can be done in real time.     

A note on ‘curable’ shock processes

In most conventional shock models, the events caused by an external shock are initiated at the moments of its occurrence. Recently, Cha and Finkelstein (2012) had considered the case when each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in the classical shock models, but with delay of some random time. In this paper, we suggest the new type of shock models, where each delayed failure can be cured (repaired) with certain probabilities. These shock processes have not been considered in the literature before. We derive and analyze the corresponding survival and failure rate functions and consider a meaningful reliability example of the stress–strength model.     

基于车牌识别数据的城市交通流时空特性分析

了解城市道路交通流的时空特性有助于提高交通流的预测精度。基于实测的车牌识别数据,运用相似系数、快速傅氏变换和混沌理论分析交通流相似性、周期性和混沌性的时间特性;运用相关系数及互相关函数作为度量标准对交通流空间特性进行描述,论证交通流检测断面之间存在空间相互作用并具有时滞性;根据交通流的空间相关性,使用多维标度法对实际路网中检测断面进行聚类和分组,为交通流预测中的多断面分组以及构建交通流时空预测模型提供理论基础。     

Bivariate Constant-Stress Accelerated Degradation Model and Inference

To assess the reliability of highly reliable products that have two or more performance characteristics (PCs) in an accurate manner, relations between the PCs should be taken duly into account. If they are not independent, it would then become important to describe the dependence of the PCs. For many products, the constant-stress degradation test cannot provide sufficient data for reliability evaluation and for this reason, accelerated degradation test is usually performed. In this article, we assume that a product has two PCs and that the PCs are governed by a Wiener process with a time scale transformation, and the relationship between the PCs is described by the Frank copula function. The copula parameter is dependent on stress and assumed to be a function of stress level that can be described by a logistic function. Based on these assumptions, a bivariate constant-stress accelerated degradation model is proposed here. The direct likelihood estimation of parameters of such a model becomes analytically intractable, and so the Bayesian Markov chain Monte Carlo (MCMC) method is developed here for this model for obtaining the maximum likelihood estimates (MLEs) efficiently. For an illustration of the proposed model and the method of inference, a simulated example is presented along with the associated computational results.     

Reliability Evaluation for A Class of Multi-Unit Cold Standby Systems under Poisson Shocks

The reliability evaluation for a multi-units cold standby system with a switch-over under Poisson shocks is investigated. The random value of each shock is assumed to be i.i.d. with some known distribution. Each arrival of a shock has a random effect on the operating unit and on the switch-over. When the operating unit fails while the switch-over is normal, the next cold standby unit will start to operate immediately. The system fails only when all the units have failed or both the operating unit and the switch-over have failed. The reliability function and the mean time to the failure (MTTF) of the system are obtained.     

Using Adjacent-category Logits Procedure for Estimating Receiver Operating Characteristic Surface

This article presents a semiparametric method for estimating receiver operating characteristic surface under density ratio model. The construction of the proposed method is based on the adjacent-category logit model and the empirical likelihood approach. A bootstrap approach for the VUS estimator inference is presented. In a simulation study, the proposed estimator is compared with the existing parametric and nonparametric estimators in terms of bias, standard error, and mean square error. Finally, a real data example and some discussions on the proposed method are provided.