Convergence Refinement Of The Fluid Approximation For The Sojourn Time In A Two Stage Tandem Queue

This paper starts with the basic knowledge of queuing theory,gives the basic definitions needed for subsequent proofs,and then introduces a single-serving queue system model under a first-come-first service rule,the corresponding system equations and its fluid approximation form.On this basis,the following two aspects of research are mainly carried out:1.The customer's stay time process in a two-service tandem queuing system with a single class of customer arrivals under a first-come,first-served basis.The two refined analysis results of the fluid approximation of the customer's stay time process under the system model are mainly proved:1.The fluid approximation satisfies the law of the iterated logarithm;2.The fluid approximation has the exponential convergence rate.2.The stay time process of customers in a single-service desk queuing system with two types of customer arrivals under a first-come,first-served basis.It is mainly proved that the fluid approximation has an exponential convergence rate.The paper proves that the fluid approximation of the customer's stay time process under the system model is a good approximation,that is,the fluid approximation using the customer's stay time process in the analysis and optimization of the system can also replace the customer's stay time process.Achieving a better reduction of the original process,making the analysis more simplified,provides a theoretical basis for the use of fluid approaching to study the original process,and also provides a possibility for the study of the corresponding problem in the promotion model.