In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using...In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.展开更多
According to the rock engineering property and stability of high-steep open-pitslopes, various factors were collected on the basis of rock engineering system (RSE) theory,and the interaction matrix of stability evalua...According to the rock engineering property and stability of high-steep open-pitslopes, various factors were collected on the basis of rock engineering system (RSE) theory,and the interaction matrix of stability evaluation was established.Then, the stabilityevaluation index (S_p) of the slope was put forward.Ranges of the S_p value and the correspondingstable state were given on the basis of thirty-six samples.It is found that the followingrelationships exist: unstable (easy landslide): S_p<-0.20; mid-stable (may be landslide):-0.20<S_p<0.63; stable (no landslide): S_p>0.63.Finally, the stability evaluation indexwas applied on the high-steep open-pit slope of one mine.Analysis results and monitoringdata indicate that the index meets the necessity of the property of slope engineering, and ithas an important engineering purpose for landslide forecasting of high-steep slopes.展开更多
We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions for n-type Markov branching processes on the basis of the 1-type Markov branching pr...We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions for n-type Markov branching processes on the basis of the 1-type Markov branching processes and 2-type Markov branching processes. Investigating such behavior is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for n-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λC of such model is given for the communicating class C = Zn+ \ 0. It is shown that this λC can be directly obtained from the generating functions of the corresponding q-matrix. Moreover, the λC -invariant measures/vectors and quasi-distributions of such processes are deeply considered. λC -invariant measures and quasi-stationary distributions for the process on C are presented.展开更多
We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the i...We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the intensity matrices and the deviation matrix, respectively. Moreover, we obtain perturbation bounds on the stationary distributions, which extends the results by Liu(2012) for uniformly bounded CTMCs to general(possibly unbounded) CTMCs. Our arguments are mainly based on the technique of augmented truncations.展开更多
文摘In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.
基金Supported by the National Natural Science Foundation of China(50874042)
文摘According to the rock engineering property and stability of high-steep open-pitslopes, various factors were collected on the basis of rock engineering system (RSE) theory,and the interaction matrix of stability evaluation was established.Then, the stabilityevaluation index (S_p) of the slope was put forward.Ranges of the S_p value and the correspondingstable state were given on the basis of thirty-six samples.It is found that the followingrelationships exist: unstable (easy landslide): S_p<-0.20; mid-stable (may be landslide):-0.20<S_p<0.63; stable (no landslide): S_p>0.63.Finally, the stability evaluation indexwas applied on the high-steep open-pit slope of one mine.Analysis results and monitoringdata indicate that the index meets the necessity of the property of slope engineering, and ithas an important engineering purpose for landslide forecasting of high-steep slopes.
基金supported by National Natural Sciences Foundation of China (Grant No.11071259)Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110162110060)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No. 2010QYZD001)the Graduate Degree Thesis Innovation Foundation of Hunan Province (Grant No. CX2011B077)
文摘We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions for n-type Markov branching processes on the basis of the 1-type Markov branching processes and 2-type Markov branching processes. Investigating such behavior is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for n-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λC of such model is given for the communicating class C = Zn+ \ 0. It is shown that this λC can be directly obtained from the generating functions of the corresponding q-matrix. Moreover, the λC -invariant measures/vectors and quasi-distributions of such processes are deeply considered. λC -invariant measures and quasi-stationary distributions for the process on C are presented.
基金supported by National Natural Science Foundation of China(Grant No.11211120144)the Fundamental Research Funds for the Central Universities(Grant No.2010QYZD001)
文摘We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the intensity matrices and the deviation matrix, respectively. Moreover, we obtain perturbation bounds on the stationary distributions, which extends the results by Liu(2012) for uniformly bounded CTMCs to general(possibly unbounded) CTMCs. Our arguments are mainly based on the technique of augmented truncations.
