Analysis Of M/G/1 Queueing System With Server Vacation And Min(N,D,V)-Control Policy

In this thesis,we consider the M/G/1 queueing system with server vacation and vacation can be interrupted immediately according to the Min(N,D,V)-policy.The con-tent is divided into two parts as follows:(1)In Chapter 1,"single server vacation" is introduced into the M/G/1 queueing system with Min(N,D,V)-control policy.Under the single vacation rule,the server is only allowed to take a vacation when the system becomes empty.The transient and steady-state proper-ties of the system queue length under arbitrary initial state are discussed via employing the total probability decomposition technique.We also obtain the Laplace transform expression of the transient solution of queue length distribution and derive the recursive expressions of the equilibrium solution of the queue length distribution.Meanwhile,we give the stochastic decomposition results of the steady-state queue length,the explicit expressions for the discrete distribution of the additional queue length and the corresponding probability function expres-sions of the steady-state queue length distribution in some special cases.Then,the numerical examples are used to analyze the influence of different parameters of the additional average queue length on system performance.Finally,the expected cost function of the system opera-tion in the long-run per unit time is derived by establishing the cost structure model.And we numerically focus on discussing the two-dimensional optimal control policy(N*,D*)which minimizes the long-run expected cost per unit time,the three-dimensional optimal control pol-icy(N*,D*,T*)when the vacation time is fixed as T,the two-dimensional optimal control policy(D*,T*)when N?? and the two-dimensional optimal control policy(N*,T*)when D??,respectively.(2)In Chapter 2,we consider the M/G/1 queueing system with multiple adaptive vaca-tions and Min(N,D,V)-policy.That is,once the system becomes empty,the server immedi-ately will take H vacations consecutively(H is a random variable with positive integer value)according to the limitation of auxiliary workload that needs to be completed currently.By employing the total probability decomposition technique and the Laplace transformation,the transient and steady-state indices of the queuing system are obtained.Furthermore,in some special cases,the corresponding explicit expression of the average steady-state queue length distribution of the system is obtained,and the numerical example is used to analyze the im-portant effect of steady-state queue length distribution in system capacity optimization design.Finally,the cost structure model is established by using the update process theory,and the sys-tem average cost function expression generated by the system operation in the long-term per unit time is derived.And we numerically stress on determining the the two-dimensional con-trol policy(N*,D*),the three-dimensional decision variables(N*,T*)when the vacation time is fixed as T and the three-dimensional decision variables(N*,J*)when the number of consecutive vacations is fixed as J which minimize the long-run expected cost per unit time,respectively.