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
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
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
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.
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.
