First passage times for Markov renewal processes and applications  

作　　者：徐光煇 袁学明 李泉林 

机构地区：[1]Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China [2]Asian-Pacific Operations Research Center, within CAS and APORS, Beijing 100080, China [3]National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China

出　　处：《Science China Mathematics》2000年第12期1238-1249,共12页中国科学：数学（英文版）

摘　　要：This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.

关 键 词：MARKOV RENEWAL process (MRP) joint transform first PASSAGE time BUSY period BUSY cycle UNIFORM error. 

分 类 号：O211.62[理学—概率论与数理统计]