We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The co...We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.展开更多
For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-m...For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-matrix of P（t）, is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegnmnd dual of some Q-function is also given.展开更多
In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using th...In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.展开更多
配电自动化对配电网供电可靠性的贡献程度有赖于通信方式的选择。为此,提出一种基于连续时间马尔科夫链的配电信息物理系统可靠性评估方法。建立层次化的系统可靠性模型,解析各层子系统的可靠性指标传递过程,利用灵敏度分析来比较不同...配电自动化对配电网供电可靠性的贡献程度有赖于通信方式的选择。为此,提出一种基于连续时间马尔科夫链的配电信息物理系统可靠性评估方法。建立层次化的系统可靠性模型,解析各层子系统的可靠性指标传递过程,利用灵敏度分析来比较不同通信接入技术的场景适用性。最后,以罗伊-比尔顿测试系统(Roy Billton test system,RBTS)母线5为算例对所提方法进行验证,并分析网络时延和误码对供电可靠性的影响。结果表明:基于无线公网的配电自动化,在合适的信噪比条件下可达到应用光纤或电力线载波通信方式的可靠性水平。展开更多
As a payload support system deployed on satellites,the turntable system is often switched among different working modes during the on-orbit operation,which can experience great state changes.In each mode,the missions ...As a payload support system deployed on satellites,the turntable system is often switched among different working modes during the on-orbit operation,which can experience great state changes.In each mode,the missions to be completed are different,consecutive and non-over-lapping,from which the turntable system can be considered to be a phased-mission system(PMS).Reliability analysis for PMS has been widely studied.However,the system mode cycle characteristic has not been taken into account before.In this paper,reliability analysis method of the satellite turntable system is proposed considering its multiple operation modes and mode cycle characteristic.Firstly,the multi-valued decision diagrams(MDD)manipulation rules between two adjacent mission cycles are proposed.On this basis,MDD models for the turntable system in different states are established and the reliability is calculated using the continuous time Markov chains(CTMC)method.Finally,the comparative study is carried out to show the effectiveness of our proposed method.展开更多
In the field of model-based system assessment,mathematical models are used to interpret the system behaviors.However,the industrial systems in this intelligent era will be more manageable.Various management operations...In the field of model-based system assessment,mathematical models are used to interpret the system behaviors.However,the industrial systems in this intelligent era will be more manageable.Various management operations will be dynamically set,and the system will be no longer static as it is initially designed.Thus,the static model generated by the traditional model-based safety assessment(MBSA)approach cannot be used to accurately assess the dependability.There mainly exists three problems.Complex:huge and complex behaviors make the modeling to be trivial manual;Dynamic:though there are thousands of states and transitions,the previous model must be resubmitted to assess whenever new management arrives;Unreusable:as for different systems,the model must be resubmitted by reconsidering both the management and the system itself at the same time though the management is the same.Motivated by solving the above problems,this research studies a formal management specifying approach with the advantages of agility modeling,dynamic modeling,and specification design that can be re-suable.Finally,three typical managements are specified in a series-parallel system as a demonstration to show the potential.展开更多
为了将故障预测与健康管理(prognostics and health management,PHM)技术应用到工程实践中,提出了基于可用度模型的PHM方法。首先通过广义随机Petri网(generalized stochastic Petri nets,GSPN)和连续马尔科夫链(continuous time Markov...为了将故障预测与健康管理(prognostics and health management,PHM)技术应用到工程实践中,提出了基于可用度模型的PHM方法。首先通过广义随机Petri网(generalized stochastic Petri nets,GSPN)和连续马尔科夫链(continuous time Markov chain,CTMC)建立基本单元的软硬件可用度模型和健康状态转换图,通过求解微分方程得到基本单元软硬件的可用度数值。然后综合软硬件之间的故障相关性建立基本单元的完整可用度模型,并利用事件调度仿真机制得到其可用度的解。最后将基本单元故障模型同通用的可修系统稳态可用度模型对比,得到"可用度-故障率-维修率"形式的PHM计算模型,并以此作为工程应用中PHM分析的有效手段。展开更多
基金Acknowledgements The authors would like to thank Professor Yong-Hua Mao for useful discussion. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11571372, 11501576, 11771452） and the Excellent Young Scientific Research Fund of Hunan Provincial Education Department （Grant No. 15B252）.
文摘We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.
基金Supported by NSFC(Grant Nos.11626245 and 11571043)
文摘For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-matrix of P（t）, is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegnmnd dual of some Q-function is also given.
文摘为了实现同一地域范围内的众多用户在有限带宽条件下提出的高QoS要求,本文对基于IEEE 802.16标准的宽带无线接入网中数据包级QoS(Quality of Service)性能进行了研究.具体做法是,首先采用批马尔可夫到达过程(BMAP,Batch Markov Arrival Process)和连续时间马尔科夫链(CTMC,Continuous Time Markov Chain)对到达过程和流量源进行建模,得到更符合实际和更准确的排队模型;然后基于状态空间,对一个无线接入网络系统进行建模,通过对得到的系统模型并结合前面得到的排队模型的深入分析,从而获得该模型下的各项QoS性能指标,如平均队列长度、丢包率、队列吞吐量和平均包时延.仿真实验结果表明,本文提出的算法模型相比于其他典型的算法模型,能够使得各项QoS性能指标有较大的改善和提高.
文摘In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.
文摘配电自动化对配电网供电可靠性的贡献程度有赖于通信方式的选择。为此,提出一种基于连续时间马尔科夫链的配电信息物理系统可靠性评估方法。建立层次化的系统可靠性模型,解析各层子系统的可靠性指标传递过程,利用灵敏度分析来比较不同通信接入技术的场景适用性。最后,以罗伊-比尔顿测试系统(Roy Billton test system,RBTS)母线5为算例对所提方法进行验证,并分析网络时延和误码对供电可靠性的影响。结果表明:基于无线公网的配电自动化,在合适的信噪比条件下可达到应用光纤或电力线载波通信方式的可靠性水平。
基金co-supported by the Natural Science Foundation of China(No.61833016)the Shaanxi Out-standing Youth Science Foundation(No.2020JC-34)+1 种基金the Shaanxi Science and Technology Innovation Team(No.2022TD-24)the Natural Science Foundation of Heilongjiang Province of China(No.LH2021F038).
文摘As a payload support system deployed on satellites,the turntable system is often switched among different working modes during the on-orbit operation,which can experience great state changes.In each mode,the missions to be completed are different,consecutive and non-over-lapping,from which the turntable system can be considered to be a phased-mission system(PMS).Reliability analysis for PMS has been widely studied.However,the system mode cycle characteristic has not been taken into account before.In this paper,reliability analysis method of the satellite turntable system is proposed considering its multiple operation modes and mode cycle characteristic.Firstly,the multi-valued decision diagrams(MDD)manipulation rules between two adjacent mission cycles are proposed.On this basis,MDD models for the turntable system in different states are established and the reliability is calculated using the continuous time Markov chains(CTMC)method.Finally,the comparative study is carried out to show the effectiveness of our proposed method.
基金the National Natural Science Foundation of China(52105070,U21B2074)Department of Science and Technology of Liaoning Province China(2033JH1/10400007).
文摘In the field of model-based system assessment,mathematical models are used to interpret the system behaviors.However,the industrial systems in this intelligent era will be more manageable.Various management operations will be dynamically set,and the system will be no longer static as it is initially designed.Thus,the static model generated by the traditional model-based safety assessment(MBSA)approach cannot be used to accurately assess the dependability.There mainly exists three problems.Complex:huge and complex behaviors make the modeling to be trivial manual;Dynamic:though there are thousands of states and transitions,the previous model must be resubmitted to assess whenever new management arrives;Unreusable:as for different systems,the model must be resubmitted by reconsidering both the management and the system itself at the same time though the management is the same.Motivated by solving the above problems,this research studies a formal management specifying approach with the advantages of agility modeling,dynamic modeling,and specification design that can be re-suable.Finally,three typical managements are specified in a series-parallel system as a demonstration to show the potential.
文摘为了将故障预测与健康管理(prognostics and health management,PHM)技术应用到工程实践中,提出了基于可用度模型的PHM方法。首先通过广义随机Petri网(generalized stochastic Petri nets,GSPN)和连续马尔科夫链(continuous time Markov chain,CTMC)建立基本单元的软硬件可用度模型和健康状态转换图,通过求解微分方程得到基本单元软硬件的可用度数值。然后综合软硬件之间的故障相关性建立基本单元的完整可用度模型,并利用事件调度仿真机制得到其可用度的解。最后将基本单元故障模型同通用的可修系统稳态可用度模型对比,得到"可用度-故障率-维修率"形式的PHM计算模型,并以此作为工程应用中PHM分析的有效手段。
