The Machine-Repair Model With Repairmen's Performing Some Secondary Tasks

Machine-repair model is a classic application of queueing theory. As the queueing theory developing, machine-repair models had been studied first by C.Plam who researched the machine-interfere model with single repairman in 1947. Later W.Feller( 1967) expounded classic M/M/c machine-repair model, and D.Gross and C.Harris(1974) researched spares case. In order to make use of spare time, let repairmen to do secondary tasks, in this way classic machine-repair model is not suitable any more. Therefore it is necessary to study this machine-repair model with repairmen's performing some secondary task.In the thesis, the model is analyzed as a finite source queue with vacation By using the method of quasi-birth and death process, we obtain the stationary distributions of the model, and make examples to explain how the model is applied in manufacture management, then we plot some figures obviously presenting the mutual effects between the system parameters and stationary distribution. It is found that higher system efficiency achieves by exiguously adjusting the system parameters in a given area. This model has provided academic gist for scientific manufacture management.Firstly, we comprehensively introduce the basic knowledge concerning the subject and analyze the history and current situation of vacation queues. Then, we explicitly describe the model being studied, and give out the process how to obtain the transition matrix of the model. By using the method of quasi-birth and death process, we set up equilibrium equation, and gain stationary distributions of queue length, the amount of waiting customers and waiting time, also average waiting time. Finally put out examples for assistant explain. The thesis begins with machine-repair model with single repairman performing some secondary tasks, then expand to multi-repairmen case and spares case which has better applicable and compatible.