This paper aims at two problems which exist in most of repairable spare part demand models at present: the exponential distribution as the basic assumption and one typical distribution corresponding to a model. A gene...This paper aims at two problems which exist in most of repairable spare part demand models at present: the exponential distribution as the basic assumption and one typical distribution corresponding to a model. A general repairable spare part demand model built on quasi birth-and-death process is developed. This model assumes that both the operational time of the unit and the maintenance time of the unit follow the continuous time phase type distributions. The first passage time distribution to be out of spares, the first mean time to be out of spares, and an algorithm to get the minimal amount of spares under certain restrictions are obtained. At the end of this paper, a numerical example is given.展开更多
For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth an...For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth and death process is estimated in terms of the spectral gaps for these processes, and in some special cases, the estimation is sharp. With the aid of the symmetrization procedure, the result is also applied to two queueing models： M/M/1 in random environment and MIMIc with synchronous vacation.展开更多
Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the st...Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.展开更多
Network storage provides high scalability, availability and flexibility for storage systems, and is widely applied to many fields. Particularly, I/O performance is of great significance. Its application is wide and ex...Network storage provides high scalability, availability and flexibility for storage systems, and is widely applied to many fields. Particularly, I/O performance is of great significance. Its application is wide and expanding rapidly. I/O performance has already become the bottleneck of the whole performance of computer systems for a long time, and under the condition of the present computer technology, I/O performance optimization method looks especially important. In the paper, I/O performance model was analyzed based on the combination of quasi birth, death process and queuing model, and then solved the model. A number of important related performance indicators and the relationship between them were given. By the way of example, this method can show the I/O performance more accurately. Finally, we got some useful conclusions, which may be used to evaluate network storage performance, and are the basis of confirming I/O scheduling strategy.展开更多
A uniform algorithm for transient solutions of generalized quasi-birth-deathprocesses with an arbitrary initial distribution is developed in this paper. This algorithmis an effective tool for computing the transient q...A uniform algorithm for transient solutions of generalized quasi-birth-deathprocesses with an arbitrary initial distribution is developed in this paper. This algorithmis an effective tool for computing the transient queue length distributions of many queuingmodels which appear quite often in computer and communication systems. As examples,some numerical results are presented.展开更多
Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated priso...Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner＇s dilemma. In this article, a preference parameter k was introduced in the payoff matrix, wherein the value of k denotes the player＇s degree of egoism and altruism （preference）. Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how preference influences the evolutionary equilibrium and behaviors of players. The authors get the general results： egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method.展开更多
Constructing some proper functional spaces, we obtain the corresponding norm for the operator （-.L）^-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Fr...Constructing some proper functional spaces, we obtain the corresponding norm for the operator （-.L）^-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5（3）： 379-515], for transient birth-death processes.展开更多
基金Supported by National Defense Foundation of P. R. China (41319060206)
文摘This paper aims at two problems which exist in most of repairable spare part demand models at present: the exponential distribution as the basic assumption and one typical distribution corresponding to a model. A general repairable spare part demand model built on quasi birth-and-death process is developed. This model assumes that both the operational time of the unit and the maintenance time of the unit follow the continuous time phase type distributions. The first passage time distribution to be out of spares, the first mean time to be out of spares, and an algorithm to get the minimal amount of spares under certain restrictions are obtained. At the end of this paper, a numerical example is given.
基金Supported in part by Program for New Century Excellent Talents in University (NCET)973 Project (Grant No. 2011CB808000)NSFC (Grant No. 10721091)
文摘For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth and death process is estimated in terms of the spectral gaps for these processes, and in some special cases, the estimation is sharp. With the aid of the symmetrization procedure, the result is also applied to two queueing models： M/M/1 in random environment and MIMIc with synchronous vacation.
基金partially supported by NSFC(No.10171009)Research Fund for PhD Programs of MOE of China(No.20010533001)Research Fund for Educational Innovation for Doctorates of CSU(No.030602)
文摘Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.
基金Sponsored by the National Natural Science Foundation of China(Grant No. 61073047)the Fundamental Research Funds for the Central Universities(Grant No.HEUCFT1007andHEUCF100607)the State Key Laboratory of High-End Server & Storage Technology(Grant No.2009HSSA08)
文摘Network storage provides high scalability, availability and flexibility for storage systems, and is widely applied to many fields. Particularly, I/O performance is of great significance. Its application is wide and expanding rapidly. I/O performance has already become the bottleneck of the whole performance of computer systems for a long time, and under the condition of the present computer technology, I/O performance optimization method looks especially important. In the paper, I/O performance model was analyzed based on the combination of quasi birth, death process and queuing model, and then solved the model. A number of important related performance indicators and the relationship between them were given. By the way of example, this method can show the I/O performance more accurately. Finally, we got some useful conclusions, which may be used to evaluate network storage performance, and are the basis of confirming I/O scheduling strategy.
文摘A uniform algorithm for transient solutions of generalized quasi-birth-deathprocesses with an arbitrary initial distribution is developed in this paper. This algorithmis an effective tool for computing the transient queue length distributions of many queuingmodels which appear quite often in computer and communication systems. As examples,some numerical results are presented.
基金supported by National Natural Science Foundation of China(60574071)
文摘Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner＇s dilemma. In this article, a preference parameter k was introduced in the payoff matrix, wherein the value of k denotes the player＇s degree of egoism and altruism （preference）. Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how preference influences the evolutionary equilibrium and behaviors of players. The authors get the general results： egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method.
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11101040, 11131003）, the 985 Project, the 973 Project （No. 2011CB808000）, the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20100003110005）, and the Fundamental Research Funds for the Central Universities.
文摘Constructing some proper functional spaces, we obtain the corresponding norm for the operator （-.L）^-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5（3）： 379-515], for transient birth-death processes.
