Markov Skeleton Processes Two Types Of Gi/g/1 Queuing System

Markov skeleton process is a kind of comprehensive stochastic process,which is firstly put forward by Prof.Hou zhenting and his colleagues in 1997.The process contains many extant classical stochastic process models,such as Markov process,semi-Markov process, piecewise deterministic Markov process etc.They have important value in theory and application.Prof.Hou zhenting and his colleagues have successfully solved a series of classical difficult problems of transient distribution,steady-state distribution,ergodicity in queueing system, meanwhile posed many new problems and new thoughts.Recently,the theory has got further complete and perfect.In this thesis,we talk about N-Policy GI/G/1 queue system with set-up period and GI/G/1 queue system with P-Entering discipline during single server vacation.As for N-Policy GI/G/1 queue system with set-up period and GI/G/1 queue system with P-Entering discipline during single server vacation,compared with the former researches,the distribution of every parameter in this thesis is general.By the Markov skeleton process theory,which was firstly put forward by professor Hou.Zhenting etc, we study the transient and limit distribution of their queue length.In this thesis,we draw the following conclusions:Firstly,by the Markov skeleton process theory,we obtain the equations which satisfy the transient distribution of the length of N-Policy GI/G/1 queue system with set-up period {L(t),θ₁(t),θ₂(t),θ₃(t)},and prove that its probability distribution is the minimal nonnegative solution of some equations.And we study the limit distribution of {L(t),θ₁(t),θ₂(t),θ₃(t)}.Furthermore we find out a Doob skeleton process of N-Policy GI/G/1 queue with set-up period,and give the limit distribution,generalized limit distribution and the existence of invariant probability measure by the theory of Doob skeleton process and limit theory.Secondly,by the Markov skeleton process theory,we obtain the equations which satisfy the transient distribution of the length of GI/G/1 queue system with P-Entering discipline during single server vacation {L(t),θ₁(t),θ₂(t),θ₃(t)} and prove that its probability distribution is the minimal nonnegative solution of some equations.And then,by using Laplace transform,we talk about the limit distribution of M/G/1 queue system with P-Entering discipline during single server vacation.