M/G/1(Repairable)Queueing System Under Min(N,D,V)-Policy Control

In this thesis,we consider the M/G/1(repairable)queueing system under Min(N,D,V)-policy control.The content is divided into two parts as follows:(1)We study the M/G/1 queueing system with multiple server vacations and Min(N,D,V)-policy.First,by using the total probability decomposition technique and the Laplace transformation tool,the transient queue-length distribution and the steady queue-length distribution are discussed.Both the expressions of the Laplace transformation of the transient queue-length distribution and the recursive expressions of the steady queue-length distribution are obtained.Then,we present the stochastic decomposition result of the steady queue length and the explicit expression of the additional queue length distribution.Furthermore,some spe-cial cases,such as when N ?? or D??,and when p{V=?}=1 or p{V=0}=1,are discussed.Meanwhile,we analyze the influence of N and D on the system relevant param-eters,and discuss the optimization design problem of the system capacity,which indicates that the value of steady-state queue length distribution in the system capacity design.Finally,the explicit expression of the long-run expected cost rate is derived under a given cost structure.And by through numerical calculation,we determine the optimal control policy(N*,D*)for minimizing the long-run expected cost per unit time as well as compare with the single optimal N*-policy and the single optimal D*-policy.(2)We study the M/G/1 repairable queueing system under Min(N,D,V)-policy control,in which“the service station with breakdown and repair”is introduced.Then,by consider-ing the server's generalized busy period as the server's busy period,we discuss the queueing indexes of the system,the influence of N and D on the system relevant parameters and the optimization design problem of the system capacity.Under a given cost structure,the explicit expression of the long-run expected cost rate is derived.By through numerical calculation,we determine the optimal control policy(N*,D*)for minimizing the long-run expected cost per u-nit time as well as compare with the single optimal N*-policy and the single optimal D*-policy.Finally,we focus on discussing some reliability indexes of the service station,for example,the service station's first failure time,the probability that the time t is in a“generalized busy period ",the unavailability and the failure frequency of the service station.