Queuing Networks With Abandonment In Heavy Traffic

Queuing network is widely applied for the computer systems, communication systems and product processing systems,it has taked more attention of the scholars;because of the value of its own, it become one brach of the most active research.The queuing network in heavy traffic research has been mature, the model with abandonment is a wide range of models in practice, such as people wait too long in the queue,if the bottom line is longer than some customers',these customers may give up the service, leave the queue.For the steady model with abandonment,Baccelli, etc., and Stanford studied on the queue with one server and they gave integral equations of the distribution of the number. Ward and Glynn studied on the queue M/M/1 in heavy traffic, Garnett, etc. studied on the queue M/M/m in heavy traffic, Ward,Glynn and Doytchinov studied on the queue GI/GI/1 in heavy traffic.Professor Liu Jianmin studied on the queue GI/GI/m in heavy traffic.And he gave the diffusion approximation of the waiting time and the load process.This article is on the condition of heavy traffic,first time attempted to make the feature of giving up to combine to the network queue, gave the heavy traffic limit of load process.It promoted the work of the predecessors who only studied on the network queue.The first chapter describes the development of network queue in heavy traffic and shows the problems with giving up in the queue.The second chapter focuses on some basic knowledge of network queue model in heavy traffic. The characterization, quantitative targets, limit of such knowledge in heavy traffic, the third chapter is a model with abandon,give up this article can be compared. The fourth chapter is the core of the article.Described on the network model with abandonment in heavy traffic and analysised the model and gave the approximation of the load process.