The Discrete Time Geom/g/1 Queue With Second Optional Service And Vacation

Discrete-time queueing system with vocation is an important branch of Queueing Theory.Recently,there is a growing interest in the analysis of discrete-time queue due to their application in computer and communication system.In the real life,the need of the second optional service can be found everywhere.So Discrete-time queue with vocation and second optional service will be researched in the paper. By leading into broad sense service time and using the methord of imbedded Markov chains,the thesis offers transition probability matrix of the system and further deduces the steady-state queue length and other corresponding steady state quota, thus stabling the theory of stochastic decomposition of the steady-state queue length and waiting time,and then giving the special example to further verify correctness of the model ,in the end some numerical examples of the model are given to verify the significant of the model.Firstly, the paper studies the Geom/G/1 queue with no vacation and second optional service. By leading into broad sense service time and using the method of imbedded Markov chains and the transition probability matrix of the system,the paper obtained the generating function of the steady state queue length and waiting time distributions.The paper also obtained the busy period of the system.Secondly, the model above is extended, and the Geom/G/1 queue with multiple(single) vacation and second optional service is studied. By leading into broad sense service time and using the methord of imbedded Markov chains ,the paper gets the generating function for the steady state queue length and waiting time distributions and their stochastic decomposition results.Finally, some special examples of the corresponding models are given to further verify the correctness of the model. And then the numerical examples prove that our model could represent some practical problems reasonably.