The Research Of Geo/Geo/1Discrete Time Queueing System With Pseudo-faults

In this thesis, based on the classic discrete time Geo/Geo/1queueing system, thepseudo-fault is first introduced into the queueing system. Combining with vacations,negative customers, working vacations and N-policy, we establish a serial of mathematicalmodels, and analyze these models and derive several meaningful performance measures.The thesis is mainly composed of three parts except introduction as follows:Firstly, a review is presented of a discrete time Geo/Geo/1repairable queueingsystem with pseudo-fault and multiple vacations. Using the quasi birth and death chainand matrix-geometric solution method, we may gain the distribution of the stationaryqueue length. Furthermore, the distribution of systems reliability and the number ofcustomers and the waiting time of a customer in the system in steady state are researched.Some numerical examples are given for analyzing the effect of parameters on theperformance of the system.Secondly, we present a discrete time Geo/Geo/1repairable queueing system withpseudo-fault, negative customers and multiple working vacations. Using quasi birth anddeath chain and the method of matrix-geometric solution, we establish a two-dimensionalMarkov chain and then gain the distribution of the stability queue length, respectively.Furthermore, the reliability of the system is analyzed and the number of customers and thewaiting time of a customer in the system in steady state are obtained. We analyze theimpact of two killing strategies on the system comparatively and draw a concludingremark. Some numerical results are provided to illustrate the effect of the parameters onseveral performance measures.Finally, we provide a discrete time Geo/Geo/1repairable queueing system withpseudo-fault, N-policy and multiple vacations. By quasi birth and death chain, weestablish a two-dimensional Markov chain and get an one-step state transition probabilitymatrix. Then we obtain the distribution of the steady-state queue length using the methodof matrix-geometric solution. And then the number of customers at any point of time andthe waiting time of an arbitrary customer in the system in steady state are obtained. At thesame time, we analyze the reliability of the system. We give a serial of numerical results to illustrate the influence of the parameters on several performance indicators.