Optimization of steerable sensor network for threat detection

A Markov chain approach to detecting a threat in a given surveillance zone by a network of steerable sensors is presented. The network has a finite number of predetermined states, and transition from one state to another follows a Markov chain. Under the assumption that the threat avoids detection, two game theoretic problems for finding an optimal Markov chain (two surveillance strategies) are formulated: the first maximizes the probability of threat detection for two consecutive detection periods, whereas the second minimizes the average time of detection for the worst‐case threat's trajectory. Both problems are reduced to linear programming, and special techniques are suggested to solve them. For a dynamic environment with moving noise sources, the optimal Markov chain changes at each detection period, and the rate of convergence of the Markov chain to its stationary distribution is analyzed. Both surveillance strategies are tested in numerical experiments and compared one with another. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

基于运动相似性的监控轨迹聚合分析

对于监控轨迹序列集,提出一种使用运动特征发现其潜在语义内容的方法.在特征统计估计阶段,将轨迹曲线中的拐点特征加入到核密度估计过程中,得到准确平滑的方向多性态分布;使用隐马尔科夫模型估计轨迹子类中存在的串行或并行空间模式.最后以运动特征分布为基础,提出一种基于运动相似性的轨迹层次聚合模型.实验结果表明,该模型可以有效地分...     

柴油机磨损寿命的灰色马尔柯夫模型预测

基于灰色系统理论,将灰色ＧＭ（１,１）预测模型和马尔柯夫预测模型的优点结合起来,形成一个灰色马尔柯夫预测模型,拓宽了灰色预测的应用范围。特别地,这种模型的预测结果比其它随机波动性较大的数据到模型的预测结果精确得多。对柴油机磨损寿命进行预测,取得了令人满意的结果。     

两个单周期的备件存储模型

在工作寿命和修理时间之一服从一般的连续型分布,另一个服从指数分布的情形下讨论了单周期的备件存储问题,通过适当地划分系统的状态,利用Markov更新过程的理论进行了分析,建立了概率型模型,并由模型得到了最佳备件数的求法。     

炮兵群自动化指挥系统决策组织结构的 Petri 网建模与性能分析

对炮兵自动化指挥系统中决策组织的结构和能力进行了研究,建立了较为完善的各级指挥员指挥决策体系的Ｐｅｔｒｉ网模型。通过有色Ｐｅｔｒｉ网对群一级的炮兵自动化指挥系统在不同任务环境下的不同工作方式进行了建模表示和分析,引入了决策时延这一反应指挥决策体系能力的重要性能指标,并进一步运用马尔科夫链的分析方法对建立的指挥决策体系的Ｐｅｔｒｉ网模型进行定量分析,得出了量化结果,为自动化指挥系统中决策组织结构的设计和分析提供了理论根据。     

The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options

This article generalizes the dynamic and stochastic knapsack problem by allowing the decision‐maker to postpone the accept/reject decision for an item and maintain a queue of waiting items to be considered later. Postponed decisions are penalized with delay costs, while idle capacity incurs a holding cost. This generalization addresses applications where requests of scarce resources can be delayed, for example, dispatching in logistics and allocation of funding to investments. We model the problem as a Markov decision process and analyze it through dynamic programming. We show that the optimal policy with homogeneous‐sized items possesses a bithreshold structure, despite the high dimensionality of the decision space. Finally, the value (or price) of postponement is illustrated through numerical examples. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 267–292, 2015     

Dynamic policy for idling time preservation

This study aims to determine and evaluate dynamic idling policies where an agent can idle while some customers remain waiting. This type of policies can be employed in situations where the flow of urgent customers does not allow the agent to spend sufficient time on back-office tasks. We model the system as a single-agent exponential queue with abandonment. The objective is to minimize the system's congestion while ensuring a certain proportion of idling time for the agent. Using a Markov decision process approach, we prove that the optimal policy is a threshold policy according to which the agent should idle above (below) a certain threshold on the queue length if the congestion-related performance measure is concave (convex) with respect to the number of customers present. We subsequently obtain the stationary probabilities, performance measures, and idling time duration, expressed using complex integrals. We show how these integrals can be numerically computed and provide simpler expressions for fast-agent and heavy-traffic asymptotic cases. In practice, the most common way to regulate congestion is to control access to the service by rejecting some customers upon arrival. Our analysis reveals that idling policies allow high levels of idling probability that such rejection policies cannot reach. Furthermore, the greatest benefit of implementing an optimal idling policy occurs when the objective occupation rate is close to 50% in highly congested situations.     

Two novel critical shock models based on Markov renewal processes

In this paper, we investigate systems subject to random shocks that are classified into critical and noncritical categories, and develop two novel critical shock models. Classical extreme shock models and run shock models are special cases of our developed models. The system fails when the total number of critical shocks reaches a predetermined threshold, or when the system stays in an environment that induces critical shocks for a preset threshold time, corresponding to failure mechanisms of the developed two critical shock models respectively. Markov renewal processes are employed to capture the magnitude and interarrival time dependency of environment-induced shocks. Explicit formulas for systems under the two critical shock models are derived, including the reliability function, the mean time to failure and so on. Furthermore, the two critical shock models are extended to the random threshold case and the integrated case where formulas of the reliability indexes of the systems are provided. Finally, a case study of a lithium-ion battery system is conducted to illustrate the proposed models and the obtained results.     

Newsvendor problems with sequentially revealed demand information

This article analyzes a capacity/inventory planning problem with a one‐time uncertain demand. There is a long procurement leadtime, but as some partial demand information is revealed, the firm is allowed to cancel some of the original capacity reservation at a certain fee or sell off some inventory at a lower price. The problem can be viewed as a generalization of the classic newsvendor problem and can be found in many applications. One key observation of the analysis is that the dynamic programming formulation of the problem is closely related to a recursion that arises in the study of a far more complex system, a series inventory system with stochastic demand over an infinite horizon. Using this equivalence, we characterize the optimal policy and assess the value of the additional demand information. We also extend the analysis to a richer model of information. Here, demand is driven by an underlying Markov process, representing economic conditions, weather, market competition, and other environmental factors. Interestingly, under this more general model, the connection to the series inventory system is different. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 2012     

马尔可夫过程的k/N系统使用任务完成能力分析

研究了任务期间允许换件维修和备件供应时k/N系统的任务完成能力.首先,利用马尔可夫过程分析了k/N系统的状态转移过程,研究了k/N系统在特定维修保障策略下的运行过程.然后,以k/N系统固定任务时间内在正常状态停留时间的分布函数作为其任务完成概率模型,并通过全概率分解和更新过程的分析方法对任务完成概率进行求解.最后,利用任务完成概率模型在Matlab中绘制了任务完成概率随任务时间、任务量、备件携行数量以及备件平均供应时间的变化曲线,讨论并分析了对任务完成概率的影响.