机载战术网多信道S-ALOHA协议设计与分析

针对机载战术网(airborne tactical network, ATN)高动态、大尺度、节点稀疏分布、通信业务多样等特征,以及高可靠、低时延的信息传输需求,提出一种新的多信道时隙ALOHA(multi-channel slotted-ALOHA, MC-S-ALOHA) 协议。该协议采用一种基于活跃节点数量的退避机制,其竞争窗口的大小随网络中活跃节点数量的变化而自适应动态调整。针对提出的协议,通过对网络中忙碌信道数量和活跃节点数量建立二维马尔可夫链模型、对节点发送缓冲区建立一维马尔可夫链模型,理论推导了网络吞吐量、分组端到端时延和分组成功传输概率的数学表达式。仿真结果验证了理论推导的准确性,并表明该协议能够有效满足ATN的性能需求。     

预留轮询策略队列调度方案的建模和分析

设计了网络中间节点(网关和路由器)的预留轮询策略队列调度方案。对不同服务质量(qualities of service,QoS)要求的延迟敏感型和非延迟敏感型混合业务,通过调度不同业务间链路传输速率,使不同业务得到不同等级的服务;建立了混合业务预留轮询策略的队列调度三维马尔可夫排队模型,使用拟生灭过程和矩阵几何解的方法对该模型进行分析,得到了系统的主要性能指标:第一类非延迟敏感型业务和第二类延迟敏感型业务的平均队长、等待时间和吞吐量。给出了第二类延迟敏感型业务的阻塞概率等结果。     

具有阻塞影响的柔性制造系统排队网络模型

用有限容量局部库区的开排队网络模拟柔性制造系统，模型中，机床加工工件的时间服从指数分布，运送台车按照静态Ｍａｒｋｏｖ方式运送工件且运送时间服从指数分布，被阻塞的工件按照ＢＡＲ机理被处理，静态Ｍａｒｋｏｖ工件运送方式中的概率值受工件被阻塞的影响。     

认知无线电网络中授权用户参数估计

针对认知用户在频谱切换过程中无法实时地获取授权用户到达率与服务率的问题,提出了基于隐式马尔可夫模型的参数估计算法。首先利用排队论对授权用户队列进行建模与分析,推导出授权用户队列状态转移概率;其次利用能量感知算法检测授权用户队列真实状态,获得可观测序列值;然后利用隐式马尔可夫模型描述两种随机过程,即授权用户队列状态变化随机过程和可观测序列随机过程;最后利用forward-backward算法估计隐式马尔可夫模型,从而获得授权用户到达率与服务率。仿真结果表明,该方法能够实现实时的、较为精确的估计,从而实时地为认知用户选择频谱切换策略提供依据。     

基于Markov链互模拟的航天器发射任务可靠度模型

状态空间复杂、多过程并发执行和子过程反复迭代的特点, 使航天器发射工程实施全过程的任务可靠性评估难以量化. 通过构建多个并发执行的时间连续的Markov链对航天器发射工程状态转移约束关系进行描述, 采用互模拟时间等价关系简化航天器发射工程实施过程的状态空间, 利用连续时间Markov链的概率转移特性进行建模与分析, 得到了全系统、全过程的航天器发射任务可靠度模型. 数值验证表明该模型可用于航天器发射任务工期推演、可靠度评估以及薄弱环节分析.     

SINGULARLY PERTURBED MARKOV DECISION PROCESSES WITH INCLUSION OF TRANSIENT STATES

1 IntroductionMarkov decision processes (MDP) have drawn much sttention because of their capabilityin dealing with a wide range of application under UnCertainty. Many problems in operationsresearch such as resource allocation, queueing networks, and maChine replaCement etc., fit wellin the framework of Markov decision processes. Classical aPProaChes of discrete-time MDPmodels can be foUnd in Dermanll], RDssIZ], and ~e[3] among others.Because most of the systems in real life are large a…     

A Hyper-Erlang Jump-Diffusion Process and Applications in Finance

This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution. The authors give the explicit closed-form expression for the joint Laplace transform of the first passage time and the overshoot for the reflected process. Finally, the formula is applied to the ruin problem under the barrier dividend strategy and the pricing of the Russian option.     

Computational analysis of （MAP1, MAP2）/（PH1, PH2）/N queues with finite buffer in wireless cellular networks

This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks,which has two types of arriving calls-handoff and originating calls,both of which follow the Markov arriving process with different rates.The channel holding times of the two types of calls follow different phase-type distributions.Firstly,the joint distribution of two queue lengths is derived,and then the dropping and blocking probabilities,the mean queue length and the mean waiting time from the joint distribution are gotten.Finally,numerical examples show the impact of different call arrival rates on the performance measures.     

The bulk input M[X] /M/1 queue with working vacations

In this paper, we analyze a bulk input M^[X] /M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function(PGF) of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X] /M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.     

一种视频会议业务流的Gamma-Beta多重分形模型

针对计算机网络中的视频会议业务流,提出了一种新的Gamma Beta多重分形模型。这种模型基于视频会议业务流的Gamma分布特性,采用Beta分布产生多重分形的乘子。与普通的多重分形模型不同的是,新模型充分考虑了视频业务流在各个不同时间尺度的概率分布特性,确保其在不同的时间尺度上都能拟合源数据的分布。由于决定网络业务流排队分析特性的关键时间尺度是随着缓冲区的容量和节点传输速率而变化的,提出的模型能描述几乎各个时间尺度上的业务流特性,因此能适应各种不同情况的缓冲区的排队分析。最后,通过对视频业务流的仿真实验与排队分析验证了模型的有效性。     

R个修理工N-策略休假的温贮备机器维修问题的可靠度

文章研究了带有多个温贮备部件的机器维修问题,系统中有R个修理工,修理工进行N-策略休假. 同时还考虑了故障部件止步和中途退出的现象.文中利用Markov过程理论建立了系统状态概率满足的微分差分方程组, 利用矩阵理论和Laplace变换反演的方法求解出了系统故障状态概率的精确表达式,得到了系统可靠度及首次故障前的平均时间的精确表达式,并给出了数值结果.     

Discrete-time Geo/G/1 retrial queues with general retrial time and Bernoulli vacation

This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy.It is assumed that the server, after each service completion,begins a process of search in order to find the following customer to be served with a certain probability,or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition.The generating functions 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 on vacation.Finally,the author gives two stochastic decomposition laws,and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.     

THE TRANSITION PROBABILITY MATRIX OF A MARKOV CHAIN MODEL IN AN ATM NETWORK

In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.     

利用贝叶斯模型进行热参数估计

对利用Bayesian模型分析热传导反问题中的导热系数预测问题的方法进行了研究。导热系数反问题的解是其后验概率密度的数学期望,用MarkovchainMonteCarlo算法计算后验状态空间以得到未知导热系数的统计估计。方法中取导热系数的先验分布满足正态分布,似然函数中的温度数据满足稳态零均值白噪声,先验分布与似然函数相乘得到后验概率密度函数。采用Metropolis-Hasting算法进行数据采样构造Markovchain,并截取收敛后的样本进行分析。     

Convergence rates of Markov chain approximation methods for controlled diffusions with stopping

<正> This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations,a purely probabilistic approach is used.There is an added difficulty due to the boundary condition,which requires the continuity of the first exit time with respect to the discrete parameter.To prove theconvergence of the algorithm by Markov chain approximation method,a tangency problem might arise.A common approach uses certain conditions to avoid the tangency problem.Here,by modifying thevalue function,it is demonstrated that the tangency problem will not arise in the sense of convergencein probability and in L~1.In addition,controlled diffusions with a discount factor is also treated.     

Stochastic systems arising from Markov modulated empirical measures

This work is devoted to stochastic systems arising from empirical measures of random sequences (termed primary sequences) that are modulated by another Markov chain. The Markov chain is used to model random discrete events that are not represented in the primary sequences. One novel feature is that in lieu of the usual scaling in empirical measure sequences, the authors consider scaling in both space and time, which leads to new limit results. Under broad conditions, it is shown that a scaled sequence of the empirical measure converges weakly to a number of Brownian bridges modulated by a continuous-time Markov chain. Ramifications and special cases are also considered.     

Grey Markov chain and its application in drift prediction model of FOGs

1.INTRODUCTION Sincetheinterferometricfiberopticalgyroscope(FOG)wasfirstproposedbyAmericanUtahUniver sityin1976,ithasbeenattractingalotofscientific andtechnicalinterestsinsteadofthespinningwheel mechanicalgyroforitcanprovideuniqueadvantages.Withtheextensionofresearch,peoplehavebecome acquaintedwithnoisesandbiasdrifts,whichinduce non negligibleerrorsintheoutputofFOGs.The hugeeffortsontechnique,whichweredevotedtothe developmentoflow noiseandlow driftFOGsmainly basedonmaterials,machining…     

具有负顾客到达和RCH移除策略的GI/D-MSP/1/N离散时间排队系统

综合运用补充变量方法和基于条件概率矩阵迭代的嵌入Markov链方法研究了具有负顾客到达和RCH移除策略的离散时间GI/D-MSP/1/N排队系统. 获得了稳态情形下正顾客到达前夕, 任意时隙分点以及外部观测时刻的三种队长分布. 并进一步讨论了可入系统正顾客的等待时间分布. 最后通过几个特殊情形下的数值算例验证了计算方法理论分析的正确性.     

多人雪堆演化博弈在愿景驱动规则下的扩展平均丰度函数

随着博弈理论的深入研究,演化博弈模型在许多社会现象和经济问题的分析中得到了广泛应用.演化博弈模型将策略更新规则引入状态转移方程,得到相应的马尔可夫链,从而研究种群演化状态.当此马尔可夫链无吸收态时,采用平均丰度函数来研究种群演化状态.采用策略更新规则中的愿景驱动规则,通过分析马尔可夫链的平稳分布导出了扩展平均丰度函数.同时,通过将多人演化博弈模型应用于雪堆演化博弈中,得到了多人雪堆演化博弈模型的扩展平均丰度函数.采用数字分析的方式,计算分析了相应参数对平均丰度函数的影响,结合具体案例研究了参数变化如何影响企业在博弈中的行为.研究表明可以通过改变相关参数来提高合作者的占比,这一结论为在实际应用中如何调控相应参数以促进合作指出了方向.     

环形相邻2/n(F)可修系统的可靠性分析

研究了由n个部件和一个维修工组成的环形相邻2/n(F)可修系统的可靠性问题。假定每个部件的工作时间和维修时间均服从指数分布,故障部件可以修复如新,但组成系统的部件是马氏相依的。利用广义转移概率的定义和关键部件优先维修的规则,求得了该系统的状态转移概率矩阵。当n已知时,获得了该系统的可靠度等重要可靠性指标。