Research On Discrete Queuing Model And SIR Epidemic Model Based On Stochastic Process

This paper mainly studies the application of stochastic process theory in discrete queuing model and SIR epidemic model.In the first part of this paper,I set up a discrete-time queuing model with vacation state.In the queuing system,customers will estimate their expected revenue according to the system information.Then they will give responses,such as entering,leaving or quitting the system.By analyzing the transition probability of each state of the queuing model,the steady-state index of the queuing system is obtained.At the same time,the expected revenue of customers and service providers is calculated.So,the system parameters that maximize their revenue are obtained.For customers,consider the impact of their behavior on other customers,and analyze their game behavior.So as to provide a reference for the behavior of customers and service providers in the system.In the second part of this paper,a SIR Epidemic Model in random environment on complete graph is established.The parameters of state transition in the model are given.The Markov chain in the system is analyzed and proved.Finally,the large and moderate deviation principles of the epidemic model and their rate function are given.