Analysis Of M/G/1 Vacation Queuing System

Vacation queue is the extension of the classic queuing theory, which was firstly studied by Levy and Yechiali in 1975. In 1980s, vacation queue had been developed into a study direction with distinguishing features, and formed a basic theoretical framework, whose core is stochastic decomposition. It 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).To meet the application needs of many different queues, the services have been introduced to the types of customers queuing model. This paper introduces the classic without leave M/G/1 queuing system analysis methods and techniques, on this basis, with the introduction of the Start-up period closed the single vacation strategy has been a steady leader of the generating function, the waiting time distribution of LST and stochastic decomposition, and the LSL, holidays, and the initiation of the LST. These results are fully new. In the model, using stochastic decomposition method makes the vacation queue additional variables into the analysis, in order to simplify the problem.With the emergence of negative customer queuing model, a growing number of scholars conducted a study of negative customer queuing system, which was pretty much the result of the current negative customers have penetrated into traffic, machinery, and computer control and many other fields. In this paper the author to leave and the first two mechanisms together with the introduction of amendments to the negative customers M/G/1 queue system. Through L-Z transform, and use of supplementary variable transfer state analysis of the distribution of team leader and steady state and transient solution reliability, enriched the theoretical model of negative customer queuing system.