Research On Problems Of M/G/1 Queue With Vacations

Vacation queue is the expansion of the classic queueing theory. Which was first studied in 1970s. It has been developed as a study direction with distinguishing featu- res by 1980s, and formed a basic theory framework, whose core is stochastic decomp- osition. Vacation queue has been applied to all kinds of up-to-date technical fields, such as computer and communication network, flexibility manufacture system (FMS), asynchronously transfer mode (ATM) and electronic commerce (EC).Various vacati- on polices produce different models of vacation queue. Two queue models are resear- ched in this paper, one is N-policy queue with set-up time, another queue model incl- udes single vacation and N-police. These models can be applied to word life practice, and have obvious application background.The whole thesis includes four chapters. In the first chapter, we show the Deve- lopment history and application background of the queue theory, and the research actuality. In the second chapter, we show basic structures of queue system and usually used methods, and list some theorems we will use. In the third chapter, we analyze the N-policy queue with set-up time, present a quantity analysis for the problem of syste- mic cost, and develop an optimal policy N* which makes the total cost least. In the last chapter, we give a new queue system, in which single vacation and N-police is considered simultaneously, and get the stochastic composition of steady-state queue length of the queueing system by stochastic composition theorem using the method of imbedded Markov chains and generating function. Moreover we analyze the busy period, vacation period and busy circulation of the system, and derive the LST of the steady-state waiting time. The latter two chapters are the core of the text.