Equilibrium Strategy Of Queuing System With Different Vacation Strategies And Two Types Of Breakdown

In recent years,with the continuous development of computer technology and the widespread application of random service processes,the study of queuing theory from the perspective of economics has become a hot issue.Since customers will pursue the maximization of their own interests,a mutual game between customers will be formed to create a balanced situation,which will affect the overall benefits of society.There are two types of failure in the system: one is the complete failure.The service desk will immediately stop the service and get repaired after the failure occurs;the other one is the incomplete failure.The service desk will serve all the customers in the system at a lower service rate and then get repaired.This paper mainly considers the problem of customers’ joining strategy and average social benefit in a queuing system with different vacation strategies and failure characteristics under fully observable conditions.This paper analyses the economic issues in the following three models.Model 1 considers two vacation strategies,which means startup time and N-policy,as well as complete breakdown.Using the Markov process,through iterative method and solving the difference equation,the steady state probability of each state in the system is obtained,and the equilibrium strategies of customers and social average benefit are given.Model 2 studies the queuing system with N-policy and two types of failure.In this system,the system will start until the number of customers in the system accumulates to N,but the system may have two types of failures at any time.By solving the difference equations and simultaneous equations,the probability distribution of the system in the steady state is solved,and the customers’ joining strategies and the average social benefit are discussed.Model 3 focuses on a queuing system with startup time and two types of breakdowns.In this situation,the system needs a period of startup time to serve customers.With steady state analysis and equilibrium analysis,the equilibrium strategies of customers and average social benefit are obtained.In the three models,the sensitivity of customer joining strategies and social average benefit to the parameters in the system are studied.