Several Researching Results Of Stochatic Severice System And Stochastic Wave

This dissertation is devoted to the study of several stochastic models of stochastic vacation service system including the continuous time multiple adaptive vacation queueing models and the discrete-time multiple adaptive vacation queueing models, and solutions to severval classes of stochastic partial differential equations describing the movement of water wave and photon. The main results, obtained in this dissertation, may be summarized as follows:1. Chapter 2, we mainly study the continuous time multiple adaptive vacations M~x/G/1 queueing model and continuous time M/G/1 queueing model with multiple adaptive vacations and set-up time. For the first model, the stochastic decompositions of steady-state queueing length and steady-state waiting time are analyzed by introducing supplementary variable parameters, and busy period is discussed. For the second model, the distributions of the steady-state queueing length and steady-state waiting time are analyzed by using the probability generating functions and the LST, and associating stochastic decomposition theorems are proved. Also closure properties of the PH-distributions with the additional length and the additional delay-time are given. Besides, the busy period, the whole vacation period and the on-line period of system are presented. Moreover, we discuss three special examples of M/G/l queue with multiple adaptive vacations and set-up times.2. Chapter 3, we study discrete-time Geom~x/G/1 queueing model with multiple adaptive vacations and discrete-time Geom/G/1 queueing model with multiple adaptive vacations and set-up time. With regarding the number of customers immediately leaving and retarding in the system as the top of observation, we give the imbedded Markov chain in which the customer arrived and its transition probability matrix. The stochastic decompositions of steady-state queueing length and steady-state waiting time are analyzed by using conditional probability and generanting function method, and busy period, whole vacation period and on line periods of model are discussed. Also the PH-distributions of the additional length and the additional delay-time of the multiple adaptive vacations and set-up time Geom/G/1 queueing model are given. Moreover,we discuss three special examples of Geom/G/1 queue with multiple adaptive vacations and set-up times.3. Chapter 4 is devoted to the study of the stochastic partial differential equations. Under the theory framework of the stochastic partial differential equations, solutions to several kinds of Wick-type stochstic partial differential equations are analyzed by special truncation expansion method, homogeneous balance method, symmetry reduction and tanh-function method, respectively.