The Research Of Repairable System With One Customer Served By Multipie Servers Simultaneously

The repairable queue system with multiple servers has been used widely in real life.It is common in Communication, Computer and other modern high-tech fields. We havestudied that one customer is in the service of one server in the repairable queue systemwith multiple servers. But there are many phenomena that a customer may be served bymultiple servers at the same time, such as breakdown machine can be repaired by manyservers, and multiple loading and unloading machines server a container at a time. So ithas important practical significance in the research about the repairable queue system withmultiple servers, a customer being served by multiple servers at the same time. The papermainly studies the repairable queue system with multiple servers that one customer isserved by multiple servers at the same time. Three different models are structured andcompared.Firstly, the article analyzes the model that on the basis of the M/M/m/N repairablequeue system, one customer being served by multiple servers at a time. The steady-stateprobabilities are obtained by the matrix analytical method, and numerical examples of thesteady-state probabilities are obtained by Matlab. In addition, we develop a cost model todiscuss the impact of the service rate and the failure rate on the performance indexes of thesystem, and get the optimal service rate.Secondly, this paper studies the repairable system with spare servers, based on therepairable queue system that one customer is served by multiple servers at a time. Thematrix equations of steady-state probabilities are obtained by the matrix analytical method,and numerical examples of the steady-state probabilities are obtained by Matlab.Furthermore, the paper develops a cost model and analyzes the influence of the servicerate and the failure rate on each optimized index, then analyzes and contrasts the one withspare servers with another with no spare servers.Finally, based on M/M/m repairable system, we has put forward the transitiondiagram, on the condition that multi-service machines serve the same customer and thearrival rate is variable. We use the matrix-geometric solution method and give the iterate formula of matrix and get the numerical example. This paper analyzes the influence of theservice rate and the failure rate on each optimized index in the end.