Queue System GI/PH/1 With Repairable Service Station

With the development of contemporary science and technology, the models made in classical queuing theory are not enough to reflect the objective fact. Many fields, such as the complicated computer communication network, information superhighway, the computer integrated manufacture system (CIMS),flexible manufacturing and assembly system, etc., have all put forward a large number of queuing theory questions. In recent years, as the development and extension of classical queuing system, repairable queuing systems have become the main content of study in queuing theory. This is mainly because that these queuing models arc more identical with realistic systems, so there are more extensive application prospects.In this thesis, we study the queuing system GI/PH/1 with repairable service station systematically, where the lifetime and the repair time of the service station are both PH random variables. This is a new repairable queuing model, and it's the promotion of the models in existing literatures. First, we prove that this queuing system can be transformed into the classical queue model GI/PH/1, then, we use the theory of matrix-geometric solutions and the method of matrix-exponential to give several indexes under stationary state. In addition, we give a unified treatment for renew service and cumulative service.This thesis is divided into four chapters. In the first chapter, we describe the development history and application status of the classical queuing system and the repairable queuing system. In the second chapter, we introduce the closed nature and update process of phase-type distribution. In the third chapter, we discuss the queuing system GI/PH/1 with repairable service station, and transform this model to a classical GI/PH/1 model to research, and give a unified treatment for renew service and cumulative service. In the fourth chapter, we use the theory of matrix-geometric solutions and the method of matrix-exponential to give the queuing indexes and reliability indexes under stationary state, and prove the queue length and the waiting time are both generalized PH variables.