Two Kinds Of Repairable Line Up The System Steady Distribution Conditions Of Research

Queuing theory is a subject that studies the crowing phenomenon. By studying the probabilistic characteristics of various kinds of service systems waiting in line, it can provide guidance to the optimal design and the optimal management strategy. In nowadays, Queuing theory has been widely used in all areas of life, steady-state condition of Queuing theory is an important content of the study of this theory.In the study of Queuing theory, the stability index of queuing system is what we should often take into account. Only if does queuing system meet the existence conditions of steady distribution, the study of its steady index could make sense. The first question should be cleared when studying any queuing system is steady-state condition. It has already had a clear conclusion of steady-state condition about the standard birth and death, but there are little studies of steady-state condition about repairable queuing system. So it has an extensive research space.In this paper, we study the multi-server repairable queuing system and repairable queuing system with two different servers. Aiming at the breakdown of servers in the multi-server repairable queue system, quasi-birth-death process theory can be used to prove the algebraic form of steady-state condition of repairable queue system so as to prove its consistency with standard queuing system in steady-state condition. For repairable queue system with two different servers, we can assume that Server A is perfectly reliable and Server B is subject to breakdown. Quasi-birth-death process can be used to work out the steady-state condition and matrix-geometric solution of the steady-state probability vectors.Some performance measures of the system and numerical illustrations are presented.