| This dissertation consists of two parts. The first part is the first Chapter, in which three models of nonlinear time series in random environment are established .In the 1980's, for the purpose of generalizing the nonlinear time series model, H. Tong and K. S. Lim have put forward a nonlinear time series model similar to the model 1 as indicated above in nature. However, till now, the research has not been under way on the limit behavior of the iterative sequence of this model. Model 2 is a brandnew time series model, which is extension of Model 1. Model 3 is the generalization of Model 1 and Model 2.The difference between the three models as indicated above and the general nonlinear time series models lies in the fact that the three new models reflect the factors of the interference in a system as well as the system itself influenced by sudden environment change. Therefore, the three new models can better imitate many substantial problems in the real world. What this difference causes in maths is that the iterative sequence of the common nonlinear time series model develops one Markov chain on general state space or multiple Markov chain, while the iterative sequence of nonlinear time series models 1,2,3 in random environment have not possessed such better nature. The former can easily be settled by applying the theory of Markov chains on general state space. In the current documents about nonlinear time series analysis, suchmethod is adopted in the papers which deal with the ergodicity of the nonlinear time series while such method cannot be adopted directly for the new three models. The first chapter serves the purpose of studying the limit behavior of the iterative sequence of the nonlinear time series in random environment. ?1, ?2 and ?3 of this chapter deals respectively with the limit behavior of the iterative sequence defined by models 1,2,3, and provide some sufficient conditions for their convergence.Part two is the second chapter, in which four queueing models are established . In the queueing models studied further so far, the least restricted so -called GI/G/1 queue in the input and service processes can be regarded as special example of the above four models. In queueing theory, the research on GI/ G/l queue have been continued for decades of years. By the end of last century , the integral representation of its transient distribution of the queue length has been obtained. In this integral representation, the integrated term can be determined recursively by a system of Kolmogorov differential equation.The purpose of the second chapter is to establish the integral representation of the transient distribution of the queue length of these four queueing models which are more general than GI/G/1 queueing system. 3,4,5 and ?6 of this chapter deal respectively with the transient distribution of the queue length of these four queueing systems. Such results are obtained as follows:Under the condition of the interarrival times distributions and service times distributions of these queueing models which have density function, their transient distribution of the queue length can be represented as an integral, and the integrated term of this integral can be recursively obtained. These results are similar to those of the transient distribution of queue length about GI/G/1 queueing system.Additionally, provided that not all interarrival times distribution and ser-vice times distribution are of density function, the integral representation of the transient disribution of the queue length of these four queueing systems as indicated above is obtained by applying the theory of Markov skeleton processes.In dealing with the two strikingly different parts as indicated above, the similar method are adopted. This method, in this paper, is called " Mark-ovnization", that is, proper supplementary variables are added to an non -Markov process,then a new process can be obtained, which is a Markov process . Therefore, this new process can be analyzed by applying the theory o...
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