First passage times and their algorithms for markov processes

Abstract

For a general Markov process on a denumerable state space with any initial state probability vector, the vectors of density functions of the first passage times to each state of a given set and their LS transforms are obtained and their algorithms are discussed. Some numerical examples are presented. These results are useful in studying busy periods and waiting times in queues

Keywords:

• Denumerable state Markov process
• first passage time
• uniformization technique
• uniform error