Discrete-time Markov-based dynamic control approach for compressed sampling

To solve the problem that the signal sparsity level is time-varying and not known as a priori in most cases,a signal sparsity level prediction and optimal sampling rate determination scheme is proposed.The discrete-time Markov chain is used to model the signal sparsity level and analyze the transition between different states.According to the current state,the signal sparsity level state in the next sampling period and its probability are predicted.Furthermore,based on the prediction results,a dynamic control approach is proposed to find out the optimal sampling rate with the aim of maximizing the expected reward which considers both the energy consumption and the recovery accuracy.The proposed approach can balance the tradeoff between the energy consumption and the recovery accuracy.Simulation results show that the proposed dynamic control approach can significantly improve the sampling performance compared with the existing approach.

STATIONARITY OF A CLASS OF LARGE-SCALE DISCRETE-TIME STOCHASTIC SYSTEMS

Stationarity of a class of stochastically interconnecteil discrete-timesystems is analyzed by utilizins results from ergodic theory of general stateMarkov chains, incorporated with the so called large-scale system approach.

Formal Reasoning About Finite-State Discrete-Time Markov Chains in HOL

Markov chains are extensively used in modeling different aspects of engineering and scientific systems, such as performance of algorithms and reliability of systems. Different techniques have been developed for analyzing Markovian models, for example, Markov Chain Monte Carlo based simulation, Markov Analyzer, and more recently probabilistic model- checking. However, these techniques either do not guarantee accurate analysis or are not scalable. Higher-order-logic theorem proving is a formal method that has the ability to overcome the above mentioned limitations. However, it is not mature enough to handle all sorts of Markovian models. In this paper, we propose a formalization of Discrete-Time Markov Chain （DTMC） that facilitates formal reasoning about time-homogeneous finite-state discrete-time Markov chain. In particular, we provide a formal verification on some of its important properties, such as joint probabilities, Chapman-Kolmogorov equation, reversibility property, using higher-order logic. To demonstrate the usefulness of our work, we analyze two applications： a simplified binary communication channel and the Automatic Mail Quality Measurement protocol.

基于自适应FNN和DTMC的MOA在线故障诊断与评估方法

现阶段一般采用离线停电试验方法对氧化锌避雷器(metal oxide arrester,MOA)进行故障判断和运行评估,影响了供电可靠性。为此,基于自适应模糊神经网络(fuzzy neural network,FNN)和离散时间马尔科夫链(discrete-time Markov chain,DTMC),提出MOA在线故障诊断与状态评估方法。首先提取与MOA运行状态相关的指标参数,通过自适应FNN学习运行状态特征指标,并且自适应动态调整隶属度函数。然后基于DTMC,考虑不同时刻运行状态特征数据,计算MOA故障类型与运行状态评估概率值。最后进行实时数据仿真以及多组历史数据仿真试验,结果准确率均在90%以上,验证了所提算法的合理性和可靠性。

多层弹道导弹防御体系射击策略研究

主要利用离散马尔可夫链(DTMC)对多层弹道导弹防御系统反导作战射击策略问题进行了研究。定义了多层弹道导弹防御体系防御层识别矩阵、拦截矩阵、综合防御能力矩阵等描述多层弹道导弹防御体系防御层作战能力的相关概念,建立了多层弹道导弹防御体系的DTMC模型。在此基础上,应用多层弹道导弹防御体系的DTMC模型对多层弹道导弹防御体系射击策略对作战效能的影响进行了预测分析,最后应用实例验证了模型的有效性及实用性。研究结果可为制定多层弹道导弹防御体系射击策略问题提供决策依据。

Ad Hoc网络的离散时间马氏链建模及分析

Ad Hoc网络是一种非常有前途的自组无线网。该文通过对Ad Hoc网络作出一些合理假设，建立了Ad Hoc网络的离散时间马氏链模型，给出了模型的平稳分布，并进一步分析了节点相邻的概率、节点的平均邻居数、平均泛洪距离等网络重要参数。最后，给出了转移概率矩阵的一个具体定义方法，并得到了相应结果。

基于离散时间马尔科夫链的塔台管制员注视转移差异性研究

为研究塔台管制员在不同工作负荷下注视转移模式的差异,构建了模拟塔台管制的眼动试验平台,根据航班流量密度设计简单和困难2组试验。利用NASA-TLX量表评价被试者在2组试验中的工作负荷,应用离散时间马尔科夫链(discrete time Markov chain,DTMC)计算被试者在兴趣区间的注视一步转移概率,利用SPSS软件分析2组试验中被试在各兴趣区组的注视一步转移概率差异性。结果发现:被试者的工作负荷随航班流量密度增大而增大。航班流量密度增大后,被试者在场面监视雷达区内的注视转移显著增加,由场面监视雷达区向空域监视雷达区和指令栏区的注视转移显著减少,在进程单区内的注视转移显著增加。管制员的注意力更容易向能获取更多信息的区域发生转移。

A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH J-VACATION POLICY AND GENERAL RETRIAL TIMES

The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times.As soon as the orbit is empty,the server takes a vacation.However,the server is allowed to take a maximum number J of vacations,if the system remains empty after the end of a vacation.If there is at least one customer in the orbit at the end of a vacation,the server begins to serve the new arrivals or the arriving customers from the orbit.For this model,the authors focus on the steady-state analysis for the considered queueing system.Firstly,the authors obtain the generating functions of the number of customers in the orbit and in the system.Then,the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size.Besides,the relationship between this discrete-time model and the corresponding continuous-time model is also investigated.Finally,some numerical results are provided.

A Single-server Discrete-time Retrial G-queue with Server Breakdowns and Repairs

This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system.

Anomaly detection of user behavior based on DTMC with states of variable-length sequences

In anomaly detection, a challenge is how to model a user＇s dynamic behavior. Many previous works represent the user behavior based on fixed-length models. To overcome their shortcoming, we propose a novel method based on discrete-time Markov chains （DTMC） with states of variable-length sequences. The method firstly generates multiple shell command streams of different lengths and combines them into the library of general sequences. Then the states are defined according to variable-length behavioral patterns of a valid user, which improves the precision and adaptability of user profiling. Subsequently the transition probability matrix is created. In order to reduce computational complexity, the classification values are determined only by the transition probabilities, then smoothed with sliding windows, and finally used to discriminate between normal and abnormal behavior. Two empirical evaluations on datasets from Purdue University and AT＆T Shannon Lab show that the proposed method can achieve higher detection accuracy and require less memory than the other traditional methods.