On hazard rate processes

Hazard rate processes are discussed in the context of doubly stochastic Poisson processes. We derive an explicit expression for the reliability function corresponding to an increasing hazard rate processes with independent increments. Also, bounds are obtained for the reliability function of a system with a general hazard rate process.     

(R.Q) inventory problem with unknown mean demand and learning

We address a single product, continuous review model with stationary Poisson demand. Such a model has been effectively studied when mean demand is known. However, we are concerned with managing new items for which only a Bayesian prior distribution on the mean is available. As demand occurs, the prior is updated and our control parameters are revised. These include the reorder point (R) and reorder quantity (Q). Deemer, taking a clue from some earlier RAND work, suggested using a model appropriate for known mean, but using a Compound Poisson distribution for demand rather than Poisson to reflect uncertainty about the mean. Brown and Rogers also used this approach but within a periodic review context. In this paper we show how to compute optimum reorder points for a special problem closely related to the problem of real interest. In terms of the real problem, subject to a qualification to be discussed, the reorder points found are upper bounds for the optimum. At the same time, the reorder points found can never exceed those found by the Compound Poisson (Deemer) approach. And they can be smaller than those found when there is no uncertainty about the mean. As a check, the Compound Poisson and proposed approach are compared by simulation.     

评估航空重力系统误差及向下延拓的逆泊松半参数方法

常用航空重力系统误差事后处理方法需外部重力数据,但很多地区无外部重力数据。研究发现,半参数模型可在无外部数据时估计系统误差。先用自然样条函数为系统误差建模,后用补偿最小二乘法和光滑参数求解,最后用广义交叉核实法(不需要先验信息)选取光滑参数。将半参数模型用于向下延拓逆泊松积分,建立逆泊松半参数混合模型,既可无外部重力时估计系统误差,又可向下延拓。实验结果表明:无外部重力时逆泊松积分和最小二乘配置法受系统误差影响最大,向下延拓精度最差;正则化算法可减弱系统误差影响,向下延拓精度较好;逆泊松半参数混合模型可估计系统误差,向下延拓精度最好。     

基于B样条的手指静脉结构描述方法*

针对现有手指静脉结构描述方法无法充分描述手指静脉结构中具有显著性和稳健性的线结构的问题,提出一种基于B样条的手指静脉结构描述方法。对于细化后的手指静脉纹路,该方法首先采用线段扫描方式获取各静脉分支上目标点的坐标集合,然后采用B样条曲线拟合各条静脉分支,最后求取各B样条曲线的控制点坐标,用其描述手指静脉的线结构。结果表明,采用本文方法描述手指静脉结构误差小、存储空间占用小,可以有效描述手指静脉线结构,并提高手指静脉的识别率。     

Warranty costs: An age‐dependent failure/repair model

An age‐dependent repair model is proposed. The notion of the “calendar age” of the product and the degree of repair are used to define the virtual age of the product. The virtual failure rate function and the virtual hazard function related to the lifetime of the product are discussed. Under a nonhomogeneous Poisson process scenario the expected warranty costs for repairable products associated with linear pro‐rata, nonrenewing free replacement and renewing free replacement warranties are evaluated. Illustration of the results is given by numerical and graphical examples. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Dynamic service rate control for a single‐server queue with Markov‐modulated arrivals

We consider the problem of service rate control of a single‐server queueing system with a finite‐state Markov‐modulated Poisson arrival process. We show that the optimal service rate is nondecreasing in the number of customers in the system; higher congestion levels warrant higher service rates. On the contrary, however, we show that the optimal service rate is not necessarily monotone in the current arrival rate. If the modulating process satisfies a stochastic monotonicity property, the monotonicity is recovered. We examine several heuristics and show where heuristics are reasonable substitutes for the optimal control. None of the heuristics perform well in all the regimes and the fluctuation rate of the modulating process plays an important role in deciding the right heuristic. Second, we discuss when the Markov‐modulated Poisson process with service rate control can act as a heuristic itself to approximate the control of a system with a periodic nonhomogeneous Poisson arrival process. Not only is the current model of interest in the control of Internet or mobile networks with bursty traffic, but it is also useful in providing a tractable alternative for the control of service centers with nonstationary arrival rates. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 661–677, 2013     

基于反正切函数的测试性分配方法

针对现有主流测试性分配方法存在的分配指标过低和过高等不合理问题,分析认为其根源在于现有方法采用线性分配函数,而该函数不符合测试性指标提升规律,为此,构造了一种基于反正切函数的测试性分配函数,设计故障检测率与故障隔离率指标的分配算法,开展案例应用并与经典故障率分配法和综合加权分配法进行对比分析,结果表明随着分配权重(故障率)的变大,本方法分配指标的增幅逐渐减小,不会出现极低指标和超1指标的不合理情形。     

基于梯度直方图的交叉点检测方法

提出基于梯度直方图的交叉点检测方法:统计像素点邻域梯度信息生成特征描述子,通过判定准则筛选候选交叉点,基于欧氏距离对候选交叉点进行聚类后,利用灰度加权法定位图像交叉点坐标。仿真实验验证了算法的正确性与可行性,结果表明:该方法适用于交叉角为65°～90°范围内的交叉点检测,定位精度优于0.6像素,检测率大于90%;该方法可以很好地抵抗图像旋转,定位精度和检测率基本不受图像旋转影响。该方法具有良好的抗噪性能,可满足一般透视变换下的图像交叉点检测需求,适用于结构光三维重建中的系统标定和形貌测量。     

基于相位估计的湍流降质图像盲复原

地基望远镜观测的空间目标图像受大气湍流的影响,其分辨率受到很大的限制。为了提高湍流降质图像的复原效果,提出一种改进的盲解卷积方法。首先,考虑观测图像受到高斯噪声和泊松噪声的干扰,推导出基于混合噪声模型的盲解卷积代价函数;然后,根据傅里叶光学原理,利用波前相位表示点扩展函数,将点扩展函数从像素值估计转换为参数估计;最后,通过参数化表示方式,将代价函数寻优从约束最优化问题转换为无约束最优化问题。模拟实验结果验证了本文模型与数值算法的有效性。     

Optimal inventory policies in contagious demand models

In the past, contagious distributions have been successfully applied in bacteriology, entomology, and accident statistics. This paper applies the notion of contagious distributions in the inventory control of new products and seasonal or style goods, which have an lying “true contagion” for their demands, namely, the influence of past demands on occurrence of demands. A contagious distribution is derived by assuming a nonstationary Poisson process where the demand rate at any instant depends on the past demands to that instant. Using this contagious distribution, an inventory model is developed seasonal goods and new product lines. Optimal order policies as a function of the initial level and the review period are derived.     

脉冲轮廓建模仿真与去噪

脉冲轮廓是脉冲星的一个重要物理特性,是脉冲星导航的关键观测量。为深入研究脉冲轮廓的理论特性,建立了脉冲星的标准脉冲轮廓数学模型与观察脉冲轮廓数学模型,用指数函数拟合了蟹状星云脉冲轮廓的轮廓函数,并以此为基础模拟了蟹状星云的标准脉冲轮廓。通过模拟非齐次泊松随机打靶实验获得了光子到达时间的仿真测量值,模拟了蟹状星云的观察脉冲轮廓,仿真结果表明该模型能很好地描述巡天观测的脉冲轮廓。对含噪声的脉冲轮廓进行小波阈值去噪,通过数值分析,认为GCV阈值去噪方法对观测脉冲轮廓有很好的去噪效果。     

An MX/G/1 queueing system with disasters and repairs under a multiple adapted vacation policy

We consider a queueing system with batch Poisson arrivals subject to disasters which occur independently according to a Poisson process but affect the system only when the server is busy, in which case the system is cleared of all customers. Following a disaster that affects the system, the server initiates a repair period during which arriving customers accumulate without receiving service. The server operates under a Multiple Adapted Vacation policy. The stationary regime of this process is analyzed using the supplementary variables method. We obtain the probability generating function of the number of customers in the system, the fraction of customers who complete service, and the Laplace transform of the system time of a typical customer in stationarity. The stability condition for the system and the Laplace transform of the time between two consecutive disasters affecting the system is obtained by analyzing an embedded Markov renewal process. The statistical characteristics of the batches that complete service without being affected by disasters and those of the partially served batches are also derived. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 171–189, 2015     

Discrete compound poisson processes and tables of the geometric poisson distribution

This paper discusses the properties of positive, integer valued compound Poisson processes and compares two members of the family: the geometric Poisson (stuttering Poisson) and the logarithmic Poisson. It is shown that the geometric Poisson process is particularly convenient when the analyst is interested in a simple model for the time between events, as in simulation. On the other hand, the logarithmic Poisson process is more convenient in analytic models in which the state probabilities (probabilities for the number of events in a specified time period) are required. These state probabilities have a negative binomial distribution. The state probabilities of the geometric Poisson process, known as the geometric Poisson distribution, are tabled for 160 sets of parameter values. The values of mean demand range from 0.10 to 10; those for variance to mean ratio from 1.5 to 7. It is observed that the geometric Poisson density is bimodal.     

混合排队规则的战术装备维修保障系统分析

首先将战术装备维修保障过程描述为M/M/c/k混合规则的排队过程,其损坏装备到达服从相互独立的泊松分布,维修时间服从相互独立的指数分布。同时考虑系统的到达率和维修率随系统中装备数量的变化,重要战损装备等待维修时的不耐烦性以及重要装备对一般装备的强占性优先权情况,结合战术装备维修保障系统的结构和规模,建立战术装备维修保障M/M/3/12排队模型。列出模型的平衡方程,采用矩阵的分析方法得到重要装备和一般装备的稳态分布表达式,并以队长为指标进行了系统性能的计算。     

A versatile scheme for ranking the extreme points of an assignment polytope

A cutting plane scheme embedded in an implicit enumeration framework is proposed for ranking the extreme points of linear assignment problems. This method is capable of ranking any desired number of extreme points at each possible objective function value. The technique overcomes storage difficulties by being able to perform the ranking at any particular objective function value independently of other objective values. Computational experience on some test problems is provided.     

Optimal admission pricing policies for M/Ek/1 queues

This paper extends the Low-Lippman M/M/1 model to the case of Gamma service times. Specifically, we have a queue in which arrivals are Poisson, service time is Gamma-distributed, and the arrival rate to the system is subject to setting an admission fee p. The arrival rate λ(p) is non-increasing in p. We prove that the optimal admission fee p^* is a non-decreasing function of the customer work load on the server. The proof is for an infinite capacity queue and holds for the infinite horizon continuous time Markov decision process. In the special case of exponential service time, we extend the Low-Lippman model to include a state-dependent service rate and service cost structure (for finite or infinite time horizon and queue capacity). Relatively recent dynamic programming techniques are employed throughout the paper. Due to the large class of functions represented by the Gamma family, the extension is of interest and utility.     

Control of entry to a nonstationary queuing system

In this article the control of entry of customers to a queuing system with s servers is considered. It is assumed that the arrivals form a nonstationary Poisson process with a periodic rate. The service times are assumed to be exponentially distributed with a parameter independent of time. The cost structure considered is the same as that of Naor. It is demonstrated numerically that, like the stationary cases, the average expected benefit of customers per unit of time is a unimodal function of the critical point. And, also, the social critical point is smaller than the individual critical point. These suggest the use of a search technique for finding the social critical point. The results show successful application of the discrete version of the Fibonacci search.     

相依风险下的超额赔款再保险

本文通过求二次效用函数的货币期望效用的最大值来确定自留额，认为索赔次数服从二元泊松分布，超额赔款再保险的保费按期望值原理进行计算。     

One-facility location with rectilinear tour distances

This article concerns the location of a facility among n points where the points are serviced by “tours” taken from the facility. Tours include m points at a time and each group of m points may become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. For m ≤ 3, it is proved that the objective function is separable in each dimension and an exact solution method is given that involves finding the median of numbers appropriately generated from the problem data. It is shown that the objective function becomes multimodal when some tours pass through four or more points. A bounded heuristic procedure is suggested for this latter case. This heuristic involves solving an auxiliary three-point tour location problem.     

成数超额混合再保险中最优自留额的确定

Centeno在Sparre Anderson模型中研究了调节系数关于再保险自留额的函数的性质，得到了保险人的调节系数是关于其自留额的单峰函数的结论。本文给出带扩散扰动项的复合Poisson过程的索赔时调节系数与再保险自留额的函数，得出保险公司的最优再保险自留额。