Research On Equilibrium Strategy Of Vacation Queuing System With Incomplete Information

Based on the M/ M/1 queueing model with single working vacation and multiple vacations,this paper introduces the cost function of "revenue-cost",and from the perspective of queueing economics,the steady-state distribution of the system with incomplete information and the equilibrium strategy of customers entering the queue are studied.In addition,because most of the information that customers know about the service organization is insufficient,this paper mainly considers the equilibrium strategy of the vacation queuing system under incomplete information.Compared with vacation strategies with complete information,vacation strategies with incomplete information are more complex and have more practical application background.The details are as follows:Firstly,this paper studies the queuing model with single working vacation and multiple vacations under incomplete information.In this queuing system,when the system turns from busy to empty,the service desk first enters the working vacation.During this working vacation,the service desk continues to provide services to potential customers at a low service rate.If the system is still empty after a working vacation,the service desk will enter the vacation.During the vacation,the service desk completely stops service.Until the system is not empty after a certain vacation,the service desk becomes busy.For this model,the queuing theory is used to obtain the steady-state distribution of the system under two kinds of information accuracy,which are almost unobservable and fully unobservable.Using the queuing game theory and introducing the cost function of "revenue-cost",the equilibrium strategies of customers entering the queue under two kinds of information accuracy are analyzed separately.Through numerical examples,this paper analyzes the changes of customer equilibrium strategies with parameters under different information accuracy,and finds that when the system is in a fully unobservable case,customers will adopt a compromise strategy to enter the team,that is,in the fully unobservable case,the customer's enqueue probability is greater than the minimum of the enqueue probabilities corresponding to the three states of the service desk in the almost unobservable case,and is smaller than the maximum.Secondly,this paper promotes the queuing model with single working vacation and multiple vacations,and introduces Bernoulli mechanism,that is,when the system finishes serving the last customer in the busy period,the service desk chooses to enter the working vacation with probability p and chooses to enter the vacation with probability 1-p.This mechanism enables the model to adjust the probability of entering work vacation according to the actual entry rate of customers,which enriches the theory of vacation queuing model.For this model,using queuing theory and queuing game theory,this paper studies the steady-state distribution of the system and the equilibrium strategy of customers entering the queue in three situations: almost observable,almost unobservable,and fully unobservable.Finally,through numerical examples,this paper illustrates the influence of the main parameters of the system on the customer's balanced enqueue strategy under different information accuracy.Through numerical examples,this paper finds that the customer's equilibrium strategy is more sensitive to the change of parameter p under fully unobservable case.