Network reliability for multipath TCP networks with a retransmission mechanism under the time constraint

It is essential to reduce data latency and guarantee quality of service for modern computer networks. The emerging networking protocol, Multipath Transmission Control Protocol, can reduce data latency by transmitting data through multiple minimal paths (MPs) and ensure data integrity by the packets retransmission mechanism. The bandwidth of each edge can be considered as multi-state in computer networks because different situations, such as failures, partial failures and maintenance, exist. We evaluate network reliability for a multi-state retransmission flow network through which the data can be successfully transmitted by means of multiple MPs under the time constraint. By generating all minimal bandwidth patterns, the proposed algorithm can satisfy these requirements to calculate network reliability. An example and a practical case of the Pan-European Research and Education Network are applied to demonstrate the proposed algorithm.     

Spare Reliability for Capacitated Computer Networks Under Tolerable Error Rate and Latency Considerations

Error rate and transmission time are both critical factors in a computer system. In addition to guarantee the robustness of the computer system under both tolerable error rate and latency, enhancing the system reliability by a routing scheme, named spare reliability, is also a critical task. Virtually, each branch possesses multiple possible capacities. Such a network is termed a capacitated computer network (CCN). Hence, this article develops an efficient algorithm to derive the spare reliability of a CCN, where the spare reliability is the probability that data can be sent through multiple minimal paths considering routing scheme.     

Reliability evaluation subject to assured accuracy rate and time for stochastic unreliable-node computer networks

In many real-life networks such as computer networks, branches and nodes have multi-state capacity, lead time, and accuracy rate. The network with unreliable nodes is more complex to evaluate the reliability because node failure results in the disabled of adjacent branches. Such a network is named a stochastic unreliable-node computer network (SUNCN). Under the strict assumption that each component (branch and node) has a deterministic capacity, the quickest path (QP) problem is to find a path sending a specific amount of data with minimum transmission time. The accuracy rate is a critical index to measure the performance of a computer network because some packets are damaged or lost due to voltage instability, magnetic field effects, lightning, etc. Subject to both assured accuracy rate and time constraints, this paper extends the QP problem to discuss the system reliability of an SUNCN. An efficient algorithm based on a graphic technique is proposed to find the minimal capacity vector meeting such constraints. System reliability, the probability to send a specific amount of data through multiple minimal paths subject to both assured accuracy rate and time constraints, can subsequently be computed.     

Criteria for reporting noncompartmental estimates of half‐life and area under the curve extrapolated to infinity

Various criteria have been proposed for determining the reliability of noncompartmental pharmacokinetic estimates of the terminal disposition phase half‐life (t_1/2) and the extrapolated area under the curve (AUC_extrap). This simulation study assessed the performance of two frequently used reportability rules: the terminal disposition phase regression adjusted‐r² classification rule and the regression data point time span classification rule. Using simulated data, these rules were assessed in relation to the magnitude of the variability in the terminal disposition phase slope, the length of the terminal disposition phase captured in the concentration‐time profile (data span), the number of data points present in the terminal disposition phase, and the type and level of variability in concentration measurement. The accuracy of estimating t_1/2 was satisfactory for data spans of 1.5 and longer, given low measurement variability; and for spans of 2.5 and longer, given high measurement variability. Satisfactory accuracy in estimating AUC_extrap was only achieved with low measurement variability and spans of 2.5 and longer. Neither of the classification rules improved the identification of accurate t_1/2 and AUC_extrap estimates. Based on the findings of this study, a strategy is proposed for determining the reportability of estimates of t_1/2 and area under the curve extrapolated to infinity.     

互联网统计研究

互联网发展从IT到DT已经成为必然的趋势,本文研究了DT时代的统计思维,提出互联网统计概念和互联网统计体系的基本内容,研究了面向未来发展的互联统计、互通统计、互动统计的互联网统计理论体系。考察了国际电信联盟、中国互联网络信息中心的互联网统计体系,以及国家统计局企业信息化和电子商务统计,指出存在的问题和与实际需要的巨大缺口,研究了互联网统计发展所面临的挑战,提出了我国互联网统计发展的政策建议。     

Modelling and estimating heavy-tailed non-homogeneous correlated queues: Pareto-inverse gamma HGLM with covariates

Evidence of communication traffic complexity reveals correlation in a within-queue and heterogeneity among queues. We show how a random-effect model can be used to accommodate these kinds of phenomena. We apply a Pareto distribution for arrival (service) time of individual queue for given arrival (service) rate. For modelling potential correlation in arrival (service) times within a queue and heterogeneity of the arrival (service) rates among queues, we use an inverse gamma distribution. This modelling approach is then applied to the cache access log data processed through an Internet server. We believe that our approach is potentially useful in the area of network resource management.     

Automatic starting point selection for function optimization

Traditional (non-stochastic) iterative methods for optimizing functions with multiple optima require a good procedure for selecting starting points. This paper illustrates how the selection of starting points can be made automatically by using a method based upon simulated annealing. We present a hybrid algorithm, possessing the accuracy of traditional routines, whilst incorporating the reliability of annealing methods, and illustrate its performance for a particularly complex practical problem.Now at the Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, UK.     

Small area housing stress estimation in Australia: Calculating confidence intervals for a spatial microsimulation model

This study provides small area housing stress estimates by tenure type in Australia with a way of calculating confidence intervals for a spatial microsimulation model. Findings reveal that prevalence of housing stress for private-renter, buyer, public-renter and owner households are 59.6%, 33.2%, 6.9%, and 0.3%, respectively. Almost two-thirds of these households are located in statistical local areas (SLAs) in eight capital cities, and a large number of them are in Sydney and Melbourne. Estimates for private renters and buyers are significantly high in some capitals and southeast coastal regions. About 95.7% of SLAs show accurate estimates with narrow confidence intervals.     

Preservation of some reliability properties by certain record statistics

Record values are closely connected with the occurrence times of a corresponding non-homogeneous Poisson process and in reliability theory, they are used in shock models. In this paper, first, some distribution properties of current records are presented. It is then shown that the hazard (reversed hazard) function of the upper (lower) current records can be expressed in terms of the hazard (reversed hazard) function of the parent distribution. Some reliability relationships between the original variable X and the corresponding current records and with record ranges are established. Also, preservation of some uncertainty measure based on current records is discussed.     

A simulated annealing algorithm for system cost minimization subject to reliability constraints

A simulated annealing algorithm is presented that finds the minimum cost redundancy allocation subject to meeting a minimal reliability requirement for a coherent system of components. It is assumed that components are independent of one another, and that the form of the nominal system reliability function is available for input to the algorithm     

Approximate queue length distribution of a discriminatory processor sharing queue with impatient customers

We consider a two-class processor sharing queueing system with impatient customers. The system operates under the discriminatory processor sharing (DPS) scheduling. The arrival process of each class customers is the Poisson process and the service requirement of a customer is exponentially distributed. The reneging rate of a customer is a constant. To analyze the performance of the system, we develop a time scale decomposition approach to approximate the joint queue-length distribution of each class customers. Via a numerical experiment, we show that the time scale decomposition approach gives a fairly good approximation of the queue-length distribution and the expected queue length.     

The snowball effect of customer slowdown in critical many-server systems

Customer slowdown describes the phenomenon that a customer’s service requirement increases with experienced delay. In healthcare settings, there is substantial empirical evidence for slowdown, particularly when a patient’s delay exceeds a certain threshold. For such threshold slowdown situations, we design and analyze a many-server system that leads to a two-dimensional Markov process. Analysis of this system leads to insights into the potentially detrimental effects of slowdown, especially in heavy-traffic conditions. We quantify the consequences of underprovisioning due to neglecting slowdown, demonstrate the presence of a subtle bistable system behavior, and discuss in detail the snowball effect: A delayed customer has an increased service requirement, causing longer delays for other customers, who in turn due to slowdown might require longer service times.     

Maximum likelihood and bayes prediction of current system lifetime

The Power Law Process is often used to analyse failure data of repairable systems undergoing development testing where the system failure intensity decreases as a result of repeated application of corrective actions. At the end of the development program, the system failure intensity is assumed to remain constant and the current system lifetime is assumed to be exponentially distributed. In this paper, prediction limits on the current system lifetime have been derived both in the maximum likelihood and Bayesian context. Exact values and a closed form approximation of percentage points of the pivotal quantity used in the classical approach are given in the case of failure truncated testing. For both failure and time truncated testing, the Bayesian approach is developed both when no prior knowledge is available and when information on the reliability growth rate can be given. A numerical example is also given.     

The rate of convergence to stationarity for M/G/1 models with admission controls via coupling

We study the workload processes of two M/G/1 queueing systems with restricted capacity: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not enter the system if they have to wait more than a fixed threshold time in line. For Model 1 we obtain several results concerning the rate of convergence to equilibrium. In particular, we derive uniform bounds for geometric ergodicity with respect to certain subclasses. For Model 2 geometric ergodicity follows from the finiteness of the moment-generating function of the service time distribution. We derive bounds for the convergence rates in special cases. The proofs use the coupling method.     

互联网在中国人口中的普及状况及其不均衡程度分析

一、引言自1994年中国接入互联网以来,中国互联网用户(即网民,CNNIC将其定义为平均每周使用互联网至少1小时的中国公民)的数量增长迅猛。据中国互联网络信息中心(CNNIC)最新的调查结果显示[1]:截止到2004年12月31日,中国网民人数已达9 400万人,与2003年同期相比增长了18.24%,是     

Selective Maintenance in System Reliability with Random Costs of Repairing and Replacing the Components

In this paper we consider the problem of determining the optimum number of repairable and replaceable components to maximize a system's reliability when both, the cost of repairing the components and the cost of replacement of components by new ones, are random. We formulate it as a problem of non-linear stochastic programming. The solution is obtained through Chance Constrained programming. We also consider the problem of finding the optimal maintenance cost for a given reliability requirement of the system. The solution is then obtained by using Modified E-model. A numerical example is solved for both the formulations.     

Time Series Modeling of Degradation Due to Outdoor Weathering

Environmental variables have an important effect on the reliability of many products such as coatings and polymeric composites. Long-term prediction of the performance or service life of such products must take into account the probabilistic/stochastic nature of the outdoor weather. In this article, we propose a time series modeling procedure to model the time series data of daily accumulated degradation. Daily accumulated degradation is the total amount of degradation accrued within one day and can be obtained by using a degradation rate model for the product and the weather data. The fitted model of the time series can then be used to estimate the future distribution of cumulative degradation over a period of time, and to compute reliability measures such as the probability of failure. The modeling technique and estimation method are illustrated using the degradation of a solar reflector material. We also provide a method to construct approximate confidence intervals for the probability of failure.     

Simultaneous confidence regions for the parameters of damage processes

In connection with the investigation of the reliability of products it is often necessary to consider the development of damage processes of such products to calculate parameters of reliability. The parameters of the damage process can be estimated by observations at discrete time points. If the limit level of damage is known the parameters of life distributions can be calculated by the estimated values of these parameters.     

On weighted measure of inaccuracy for doubly truncated random variables

Recently, authors have studied the weighted version of Kerridgeinaccuracy measure for left/right truncated distributions. In the present communication we introduce the notion of weighted interval inaccuracy measure and study it in the context of two-sided truncated random variables. In reliability theory and survival analysis, this measure may help to study the various characteristics of a system/component when it fails between two time points. We study various properties of this measure, including the effect of monotone transformations, and obtain its upper and lower bounds. It is shown that the proposed measure can uniquely determine the distribution function and characterizations of some important life distributions have been provided. This new measure is a generalization of recent weighted residual (past) inaccuracy measure.     

A generalized Pearson system useful in reliability analysis

In the present note, we study an extended class of Pearson system of distributions in the context of reliability. It is shown that the proposed class of models can be characterized by a relatioaship between the failure rate and the conditional moments. Further, we develop a procedure to identify an increasing (decreasing) failure rate model in the generalized Pearson system.