An M/G/1 Repairable Queueing System With Bi-level Threshold(m,N)-Policy

Based on the actual situation,this thesis introduces“the service's desk can be broken down and can be repairaed" into the M/G/1 queueing system with bi-level threshold(m,N)-policy,which makes the system model more practical and valuable.In the first chap-ter,the dissertation constructs "an M/G/1 repairable queueing system with start-up time and bi-level threshold(m,N)-policy".Firstly,by using some common computing tools such as the Laplace transform and the total probability decomposition in queuing system,we discuss some important indices of the system's running state.Then,some reliability indices,such as the unavailability of the system caused by the failure,are analyzed.Next,by numerical cal-culation,we study how the steady-state unavailability and the steady-state failure frequency of the service's desk with the variation of some system parameters.Finally,on the basis of the cost model established in this dissertation and through numerical calculation,we study the op-timal control strategy of double threshold(m*,N*)as well as compare with the optimal control policy of the queueing system that the service station doesn't fail.In the second chapter,the thesis introduces "delayed close-time" into the system studied in the first chapter,and constructs the system model of "an M/G/1 repairable queueing system with double threshold(m,N)-policy?start-up time and delayed close-time",which generalizes the system model studied in the first chapter and is more complex and difficult to study.Firstly,using the recurrence characteristics of the queue-length distribution in the server's busy period and some common calculation tools such as the Laplace transform and the total probability decomposition method in the queuing system,from any initial state we not only derive the Laplace transformation expressions of the distribution of the system's transient queue-length with respect to time t,but also get the expressions of the steady-state queue-length distribution,the probability generating function and the average queue-length.Then,the reliability indices,such as the unavailability of the system caused by the failure,are discussed in detail.Finally,on the basis of the established cost model and combined with the actual situation of the company's testing samples,we study the optimal control strategy of double threshold(m*,N*).