The Study Of Gray Queuing System And E-Convex Bilevel Programming Problem

Because of its distinctive practical background and extensive application, queuing theory has attracted a lot of attention. It is suitable for communication systems, transportation systems, computers, storage systems, production mana- gement systems and all other service systems, in which M/M/ s queue model is the basic model of many service systems. But in many practical situations, because of subjective and objective reasons, it is uncertain whether or not customers enter the system after their arrival, so the thesis focuses on gray M/M/ s queue model, which is a complete new arrival queue model. It is a hitherto unstudied project.E-convex bilevel programming is also studied. In 1999, E-convex set and E-convex function are defined by E. A. Youness, and E-convex programming is proposed. E-convex programming has become a research focus since 1999, E-convex bilevel programming is first given on the basis of E-convex programming, a new E-convex bilevel programming problem is defined, and the theorems are given.Firstly, the background, origin, development and application of the gray system theory and the queuing theory are provided, and E-convex pro- gramming research is introduced currently. Then the basic model of the bilevel decision-making system and the related knowledge are given.Secondly, the basic models of the classic M/M/ s /∞queuing system and the M/M/ s / K queuing system are described. And the stationary distributions and related indicators are given.Thirdly, combined with the characteristics of gray system on the basis of the second chapter, we analyze the basic models of the grey M/M/ s /∞and M/M/ s / K queues. Gray stationary distributions and related indicators are given. Finally,E-convex programming is extended to E-convex bilevel program- mming, and some definitions and theorems are given.