Dynamic Routing and Admission Control in High-Volume Service Systems: Asymptotic Analysis via Multi-Scale Fluid Limits

Motivated by applications in telephone call centers, we consider a service system model with m customer classes and r server pools. The model is one with doubly stochastic arrivals, which means that the m-vector λ of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of dynamic control are considered: customers may be either blocked or accepted at the time of their arrival, and then accepted customers of each class must be routed, either immediately upon acceptance or after some period of waiting, to a server pool that is qualified to handle that class. Customers who are made to wait before commencement of their service are liable to defect. The objective is to minimize the expected sum of blocking costs, waiting costs and defection costs over a fixed and finite planning horizon. We consider an asymptotic parameter regime in which (i) the arrival rates, service rates and defection rates are uniformly accelerated by a large factor κ, then (ii) arrival rates are increased by an additional factor g(κ), and the number of servers in each pool is increased by g(κ) as well. This produces a separation of time scales, justifying a pointwise stationary stochastic fluid approximation for our original system model. In the stochastic fluid approximation, optimal admission control and routing decisions are determined by a simple linear program that uses the current arrival rate vector λ as data. We explain how to implement the fluid model's optimal control policy in our original service system context, and prove that the proposed implementation is asymptotically optimal in the first-order sense. AMS subject classification: 60K30, 90B15, 90B36     

Stochastic Accelerated Alternating Direction Method of Multipliers with Importance Sampling

In this paper, we incorporate importance sampling strategy into accelerated framework of stochastic alternating direction method of multipliers for solving a class of stochastic composite problems with linear equality constraint. The rates of convergence for primal residual and feasibility violation are established. Moreover, the estimation of variance of stochastic gradient is improved due to the use of important sampling. The proposed algorithm is capable of dealing with the situation, where the feasible set is unbounded. The experimental results indicate the effectiveness of the proposed method.     

具有随机效应的Wiener加速退化模型的可靠性研究

研究了有随机效应的Wiener退化模型基于加速退化数据的统计推断问题.利用广义枢轴量方法得到了模型参数和感兴趣可靠性指标的广义置信区间.说明了不含随机效应的Wiener退化模型的统计推断问题是有随机效应的Wiener退化模型的特殊情况.蒙特卡罗模拟结果显示文中提出的区间估计有较好的覆盖比例.最后利用LED加速退化数据说...     

Optimal plan for Wiener constant-stress accelerated degradation model

This paper explores inferential procedures for the Wiener constant-stress accelerated degradation model under degradation mechanism invariance. The exact confidence intervals are obtained for the parameters of the proposed accelerated degradation model. The generalized confidence intervals are also proposed for the reliability function and pth quantile of the lifetime at the normal operating stress level. In addition, the prediction intervals are developed for the degradation characteristic, lifetime and remaining useful life of the product at the normal operating stress level. The performance of the proposed generalized confidence intervals and the prediction intervals is assessed by the Monte Carlo simulation. Furthermore, a new optimum criterion is proposed based on minimizing the mean of the upper prediction limit for the degradation characteristic at the design stress level. The exact optimum plan is also derived for the Wiener accelerated degradation model according to the proposed optimal criterion. The proposed interval procedures and optimum plan are the free of the equal testing interval assumption. Finally, two examples are provided to illustrate the proposed interval procedures and exact optimum plan. Specifically, based on the degradation data of LEDs, some interval estimates of quantities related to reliability indicators are obtained. For the degradation data of carbon-film resistors, the optimal allocation of test units is derived in terms of the proposed optimal criterion.     

Quantile regression of right-censored length-biased data using the Buckley–James-type method

Length-biased data are encountered frequently due to prevalent cohort sampling in follow-up studies. Quantile regression provides great flexibility for assessing covariate effects on survival time, and is a useful alternative to Cox’s proportional hazards model and the accelerated failure time (AFT) model for survival analysis. In this paper, we develop a Buckley–James-type estimator for right-censored length-biased data under a quantile regression model. The problem of informative right-censoring of length-biased data induced by prevalent cohort sampling must be handled. Following on from the generalization of the Buckley–James-type estimator under the AFT model proposed by Ning et al. (Biometrics 67:1369–1378, 2011), we propose a Buckley–James-type estimating equation for regression coefficients in the quantile regression model and develop an iterative algorithm to obtain the estimates. The resulting estimator is consistent and asymptotically normal. We evaluate the performance of the proposed estimator on finite samples using extensive simulation studies. Analysis of real data is presented to illustrate our proposed methodology.     

多元失效时间数据的一般边际半参数危险率模型研究

在生物医学研究中,多元失效时间数据非常常见.该文提出用一般边际半参数危险率回归模型来分析多元失效时间数据.此模型包括了三种常用边际模型:边际比例风险模型、边际加速失效时间模型和边际加速危险模型作为子模型.对于模型中的回归系数,可以通过估计方程的方法来估计它,同时也给出了基准累积危险率函数的估计.得到的估计可以证明是相合的和渐近正态的.     

An Accelerated Inexact Proximal Point Algorithm for Convex Minimization

The proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact proximal point algorithm with a new inexact criterion for solving convex minimization, and show its O(1/k) iteration-complexity. Then we show that this inexact proximal point algorithm is eligible for being accelerated by some influential acceleration schemes proposed by Nesterov. Accordingly, an accelerated inexact proximal point algorithm with an iteration-complexity of O(1/k ²) is proposed.     

Modeling of degradation data via wiener stochastic process based on acceleration factor constant principle

This paper proposes a systematic method of modeling accelerated degradation data based on the acceleration factor constant principle. Wiener stochastic process is considered because it is the most extensively used for degradation modeling. For the Wiener stochastic processes with three different time functions, the parameter relationships, which should be satisfied under any two different stress levels, are deduced according to the acceleration factor constant principle. The deduced parameter relationships indicate the stress-related parameters, which are applied to establish accurate accelerated degradation models. In addition, the deduced parameter relationships provide a guidance to test the consistency of the degradation mechanisms under different stress levels. A hypothesis method based on Analysis of Variance is adopted to identify the accelerated stress levels with different degradation mechanism. The degradation data under these stress levels should not be used to assess the product's reliability. The methods of validating accelerated degradation models and reliability assessments are also proposed. The simulation results prove the feasibility and effectiveness of the proposed methods. From the numerical example, it is concluded that the accelerated degradation model established based on the acceleration factor constant principle is more credible and accurate.     

A general additive-multiplicative rates model for recurrent event data

In this article, we propose a general additive-multiplicative rates model for recurrent event data. The proposed model includes the additive rates and multiplicative rates models as special cases. For the inference on the model parameters, estimating equation approaches are developed, and asymptotic properties of the proposed estimators are established through modern empirical process theory. In addition, an illustration with multiple-infection data from a clinic study on chronic granulomatous disease is pr...     

Adaptive Penalized Weighted Least Absolute Deviations Estimation for the Accelerated Failure Time Model

The accelerated failure time model always offers a valuable complement to the traditional Cox proportional hazards model due to its direct and meaningful interpretation. We propose a variable selection method in the context of the accelerated failure time model for survival data, which can simultaneously complete variable selection and parameter estimation. Meanwhile, the proposed method can deal with the potential outliers in survival times as well as heteroscedastic model errors, which are frequently encountered in practice. Specifically, utilizing the general nonconvex penalty, we propose the adaptive penalized weighted least absolute deviation estimator for the accelerated failure time model. Under some regularity conditions, we show that the proposed method yields consistent estimator and possesses the oracle property. In addition, we propose a new algorithm to compute the estimate in the high dimensional settings, and evaluate the practical utility of the proposed method through extensive simulation studies and two real examples.     

Hybridization of accelerated gradient descent method

We present a gradient descent algorithm with a line search procedure for solving unconstrained optimization problems which is defined as a result of applying Picard-Mann hybrid iterative process on accelerated gradient descent S M method described in Stanimirovi? and Miladinovi? (Numer. Algor. 54, 503–520, 2010). Using merged features of both analyzed models, we show that new accelerated gradient descent model converges linearly and faster then the starting S M method which is confirmed trough displayed numerical test results. Three main properties are tested: number of iterations, CPU time and number of function evaluations. The efficiency of the proposed iteration is examined for the several values of the correction parameter introduced in Khan (2013).     

A dynamic network loading model for mesosimulation in transportation systems

Flow propagation models can be divided into static and dynamic network loading models. Different approaches to dynamic network loading problem formulated in the literature point out models that can be classified as disaggregate or aggregate.Applying aggregate models, it is possible to trace implicitly or explicitly vehicles movements. The second case concerns mesoscopic models. These models consider the traffic as a sequence of “packets” of vehicles. Two approaches can be followed:

• (a)continuous packets, where vehicles are distributed inside each packet, defined by the head and the tail points;
• (b)discrete packets, where all users belonging to a packet are grouped and represented by a single point, for instance the head.

In this paper, a mesoscopic model based on discrete packets has been developed, taking into account the vehicles acceleration. The proposed model, assuming discrete packets and uniformly accelerated movement, appears lifelike in the representation of outflow dynamics and quite easy to calculate.     

一类弱非线性互补问题的广义模系矩阵多分裂多参数加速松弛迭代方法

本文提出一类求解弱非线性互补问题的广义模系矩阵多分裂多参数加速松弛迭代方法，并给出了系数矩阵为H₊-矩阵时该方法的收敛性分析.数值实验表明新方法是有效的.     

Iterative methods for convection dominated flow

Some iterative methods are considered for the numerical solution of convection diffusion problems. The first class of iterative methods is Chebyshev accelerated iterations. The issues of parameter selection and convergence rates are considered. Secondly, we consider convection—diffusion type iterations where the iterations are of Peaceman-Rachford type. Here, a conjecture is given concerning a related problem in functional analysis. Finally, we consider flow-directed iterative schemes. We describe some schemes of this class for an upwind difference method, and also for a nonlinear hyperbolic equation. We emphasize work that remains to be done on these methods.     

Time-temperature superposition. Review

Experimental attempts to confirm the applicability of time-temperature superposition as a means of predicting the deformation of polymeric materials are reviewed. Examples of the use of the method for the accelerated testing of amorphous and crystalline thermoplastics, thermosets, and composites are presented. The review is confined to the class of thermorheologically simple bodies and isothermal deformation regimes.     

一类随机多目标二次线性规划模型的交互式算法

针对线性约束条件下带有一个二次目标函数和多个线性目标函数的随机多目标决策问题，借助参考方向法和权重法对该决策问题的期望值模型进行标量化，获得了关于期望值模型的（恰当／弱）有效解的充要条件，引入Ａｃｈｉｅｖｅｍｅｎｔ函数建立了一类随机多目标二次线性规划模型的交互式计算方法．     

A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed multiple criteria decision-making (MCDM) model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.     

A modified accelerated monotone iterative method for finite difference reaction-diffusion-convection equations

This paper is concerned with monotone algorithms for the finite difference solutions of a class of nonlinear reaction-diffusion-convection equations with nonlinear boundary conditions. A modified accelerated monotone iterative method is presented to solve the finite difference systems for both the time-dependent problem and its corresponding steady-state problem. This method leads to a simple and yet efficient linear iterative algorithm. It yields two sequences of iterations that converge monotonically from above and below, respectively, to a unique solution of the system. The monotone property of the iterations gives concurrently improving upper and lower bounds for the solution. It is shown that the rate of convergence for the sum of the two sequences is quadratic. Under an additional requirement, quadratic convergence is attained for one of these two sequences. In contrast with the existing accelerated monotone iterative methods, our new method avoids computing local maxima in the construction of these sequences. An application using a model problem gives numerical results that illustrate the effectiveness of the proposed method.     

FUNCTIONAL-COEFFICIENT REGRESSION MODEL AND ITS ESTIMATION

Abstract. In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equates is suggested. This class of models,with the proposed estimation method,is a powerful means for exploratory data analysis.     

半监督距离度量学习内蕴加速投影梯度算法

考虑求解一类半监督距离度量学习问题. 由于样本集(数据库)的规模与复杂性的激增, 在考虑距离度量学习问题时, 必须考虑学习来的距离度量矩阵具有稀疏性的特点. 因此, 在现有的距离度量学习模型中, 增加了学习矩阵的稀疏约束. 为了便于模型求解, 稀疏约束应用了Frobenius 范数约束. 进一步, 通过罚函数方法将Frobenius范数约束罚到目标函数, 使得具有稀疏约束的模型转化成无约束优化问题. 为了求解问题, 提出了正定矩阵群上加速投影梯度算法, 克服了矩阵群上不能直接进行线性组合的困难, 并分析了算法的收敛性. 最后通过UCI数据库的分类问题的例子, 进行了数值实验, 数值实验的结果说明了学习矩阵的稀疏性以及加速投影梯度算法的有效性.