The Repairman Vacation Two Reception Repairable Queue System

Repairable queueing system with multi-server is a classic kind of queuing system, which means that some servers in system may go wrong and can not provide service to customers for the time being. At that time the server out of order would get repaired and continue to serve the customer once it is all right. In repairable queueing system, repairman vacation refers that system components would probably not receive repair immediately after they go wrong, because the repairman may rest or be engaged in other works. Vacation policy provides great flexibility for system optimization design and process control thus it has very important theoretical significance and practical value.In this thesis,we discuss two-sever repairable queueing system with repairman vacation and customer halt, M/(M/PH)/2repairable queueing system with repairman vacation. First,we describe the research model, obtain the infinitesimal generator and get the condition in which the Quasi-Birth-Death process is positively recurrent.Then by using the Quasi-Birth-Death process and the matrix geometric solution, we derive the various performance indicators under the steady condition. Finally the stationary probability vectors and performance indicators of the system are studied by numerical analysis through the MATLAB.