Analysis Of The Machine Repairable System With One Breakdown Machine Served By Multipie Servers

The machine repairable queue system with multiple servers has been used widely inreal life. It is common in Communication, Computer and other modern high-tech fields.We have discussed that a server gave service to one customer in the machine repairablequeue system with multiple servers. But there are many examples that a customer may beserved by multiple servers at a time. Such as port container handling problems, a containeroften needs to be served by multiple loading and unloading machines at the same time. Soit has important theoretical and practical significance in the development and applicationof queuing theory.In the article, the machine repairable system with the rule that one breakdownmachine served by multiple servers is researched. Three different models are structuredand the example analysis of each model is given respectively.Firstly, the article analyzes the M/M/R machine repair problem and assumes that abreakdown machine may be served by multiple servers at a time. The steady-stateprobabilities are obtained by the matrix analytical method with numerical examples. Inaddition, we develop a cost model to discuss the impact of the service rate on theperformance indexes of the system, and get the optimal service rate.Secondly, based on M/M/R machine repair problem, this paper has put forward thetransition diagram, on the condition that multi-service machines serve the samebreakdown machine and maintenance rate is variable. The matrix equations of steady-stateprobabilities are obtained by the matrix analytical method with numerical examples.Furthermore, the paper has developed a cost model and analyzed the influence ofmaintenance rate on each optimized index and total cost and gets the maintenance rate ofminimum total cost.Finally, we deal with the M/M/R machine repair problem with balking, reneging, andserver breakdown. In the condition that many Service machines can serve the samebreakdowns machine, we use the matrix analysis method and give the iterate formula of matrix and we make the numerical example.