Stationarity And Quasi-stationarity For PH/G/1 Queues

In this thesis,we focus on the stationarity and quasi-stationarity for PH/G/1 queues.Stochastic models with PH distribution has a very wide range of applications.We mainly investigate the polynomial ergodicity and geometric ergodicity and the existence of the quasi-stationary queue length distribution for PH/G/1 queue,and give the corresponding criteria.The main research contents are as follows:Firstly,we introduce the development and research status of queuing theory and Markov chains at home and abroad.Some preliminaries about Markov chains as well as concepts for PH distribution and PH renewal process are included.Secondly,for the stationarity problem of PH/G/1 queues,the rela-tionship between the polynomial ergodicity and the r-th order moment of customer service time is obtained by applying matrix-analytical method to the embedded Markov chain of PH/G/1 queue at the time when a cus-tomer is served.Further,the theoretical criteria for geometric ergodicity are derived by the technique of spectral analysis.Finally,for the quasi-stationarity problem of PH/G/1 queues,the criteria for geometric non-recurrent conditions of the transition matrix are obtained by matrix-analytical method.Then the existence of the quasi-stationary queue length distribution are proved,and a representation is given.0 pictures,0 tables,75 references...