M <sup> X </ Sup> / M / C ¡ú (m) / M / N / K Series Queuing System Analysis

The two-stage tandem queueing system M(x)/M/câ†'(M)/M/n/K with special customers is mainly studied in this paper. The tandem queueing system is widely used in the servicing and queueing system of bank, public service system, traffic problems, computer deployment problems and so on.The whole thesis includes four chapters. In the first chapter, the development history and stutas of the queue theory, the research background of the tandem queue model and the queue system whose custumers are arriving in batch.Simultaneously the basic content and the primary indexes of this paper are presented. In the second chapter, the basis of theoretical knowledge of the queue theory is introduced which would be used in this paper. In the third chapter,Arriving in batch and Special service of the special customers are added in the queue system M/M/1â†'M/M/1, namely M(x)/M/câ†'(M)/M/n/K.In this chapter, the transferring probability matrix of the tandem queueing system is presented by means of matrix analysis theory. The sufficient-necessary conditions for the system stability are presented by Quasi-birth-death-process theory, and the distribution of stationary queue length and its algorithm are obtained. The busy time distribution of the stage-â… ,the probability general function of the number of customers servered in busy time of the stage-â… are obtained by means of the imbedded Markov chain.And the distribution of the stage-â… service blocked time is further analyzed.The last chapter provides analysis and summary about the research subject and research progress. In addition.the further research directions are suggested.