The M/G/1 Queueing Systems With Negative Customers To Be Served And Vacations

With the rapid development of science and technology, to fit the need of application, more and more different queue disciplines, service mechanism and customer types have been applied to queueing models one after another. Vacation queue is the expansion of the classic queueing theory, which was firstly studied by Levy and Yechiali . In 1980s, vacation queues have 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).In 1990s, negative customers queueing model was firstly put forward, and furthermore it becomes a new study trend, a growing number of scholars conducted a study of negative customer queueing system. Negative customer can be seen as a assistance to the server. One assistance counteract one positive customer who is in the queue or is being served, can be described the phenomenon such as: product to be discarded as worthless because of incorrect manipulation, computer virus, system catastrophe, and so on.In the article, the author firstly studies the type of M / G /1 vacation queue system with the negative customers can be served. By using supplemental variables method and Z-transformation, we obtain the average queue length and some reliability norm in steady state.These results enrich the theory norm of negative queue model.