Equilibrium Analysis Of Fluid Queueing Model With Fault Characteristics

With the advent of the era of big data,fast has become the norm of social development.The customer fluid in the queuing system has also evolved from discrete to continuous.Such systems are modelled as the fluid queues,which have been used as the more and more widely in industries such as Internet communication and assembly line production.To avoid the system fault influence customer decision making and the social benefits of optimization,the dissertation constructs has not complete failure,complete failure,fluid queuing model disaster arrived,these models are given in the customer’s individual balking strategy and per unit time social optimal income strategies.Finally,the social income function is numerically analyzed.Firstly,the individual balking and social optimal strategies for incomplete failures fluid models are studied.The arrival process of customers in the system is independent of each other,and the system state is unstable,and failure may occur at any time.In case of failure,service will be carried out at a low rate and maintenance will be carried out immediately,during which customers are allowed to enter.The system alternates between working state and incomplete failure.The exponential payoff function is established,and the threshold value of individual balking in the completely observable and almost observable cases,the steady-state distribution of fluid level and the optimal social payoff function in unit time are obtained by solving the ordinary differential equations.Finally,the social income function is numerically analyzed,and the influence of failure maintenance rate and other parameters on social income is obtained.Secondly,the equilibrium analysis of the fault fluid queue model with two types of customers and disaster arrival is discussed.Immediately after the disaster arrives,all customers are emptied.Service is stopped and new customers are allowed to enter during the maintenance period.The arrival process of the two types of customers is independent of each other and the system alternates between full failure and working state.Customers decide whether to enter or not based on the benefit-cost utility function.The linear differential equations are constructed,and the threshold value of individual balking and the social benefit function in unit time are obtained by matrix analysis under the two information levels of fully observable and almost observable.Finally,the queuing model of fluid with complete fault is analyzed under strategy of q.When the system fails,the service will be stopped immediately and the customer can enter the maintenance state during the maintenance period.The customer is completely or partially unknowable to the information level of the buffer,so it is assumed that the fluid enters the system with the probability of q.Based on this,the individual income function is established,and whether the fluid enters the system is decided according to the positive or negative net income.Individual balking and social optimal strategies under completely unobservable and almost unobservable conditions are given.Finally,the social income function is numerically analyzed.