Gi/m/1 Queue With Set-up And Closed-down Times

Vacation queue is the expansion of the classics queueing theory, Which was first studied by Levy and Yechiali in 1975. In 1980s, Vacation queue has been developed into a study direction with distinguishing features, and formed a ba- sic theoretical framework,Whose core is stochastic decomposition. It has been applied to all kinds of up-to-date technical fields,such as,computer and commu- nication network,fiexibility manufacture system(FMS), asynchronously transfer mode(ATM) and electronic commerce(EC). In this thesis, We systems analysis GuM/i queueing system with closed- down and set-up times .This is a fully new vacation queue model . The mod- els which were studied by Tian-Naishuo(1992,1997) and Dukhovny(1997) are its special cases.With the matrix-geometric solution which Neuts and Tian-Naishuo have developed,We derive the analytic expressions of steady-state queue length and waiting time distribution. We also proved their stochastic decomposition results. The whole thesis includes four chapters. In chapter one , We indicate that this subject originates from the virtul channel analysis in ATM network and give the relationship between GI/M/1 queue model with closed-down and set-up times and connection-oriented .Furthermore, We give a concise review about the history and methods of vacation queue抯 study, Which provides a preparation for the later model analysis in theory and symbols. In chapter two,With the Markov chain imbedded in the time that the cus- tomer arrived and its transition probability matrix expressed in the block-Jocabi form, We set up the structure model of GJ/M/1 queue with closed-down and set-up times , and we discuss the sufficent and necessary condition in which the II Abstract queueing system reached equilibrium. In chapter three, By exercising structure matrix analysis and matrix-geometric solution method, We derive the queue length and waiting time distribution,and also prove corresponding stochastic decomposition theories .These results are new, And they generalized the results in the work of Tian-Naishuo(1992), Yue-Dequan(1994) and Dukhovny(1997). In chapter four ,We discuss three special examples of GI/M/1 queue with closed-down and set-up times, Which reveal the relationship between the model there studied and the work that has been done at home and abroad.