Research On Equilibrium Strategies Of Constant Retrial Queues In The Unobservable Cases

The retrial queuing model was widely used in the fields of communication net-work engineering and communication traffic theory.Considering to the limitation of equipment loss and energy consumption,the policies of set-up time and reserved time are proposed.Different strategies can be flexibly selected and the retry queuing can be combined to establish appropriate models.Through theoretical research and per-formance analysis,better suggestions can be put forward for system optimization and control.Therefore,the research on this kind of model has a good application background and important practical significance.In recent years,the study of queuing theory from the perspective of economics has become a hot issue.Each customer rationally pursues the maximization of their own interests while ignoring other customers and the system as a whole.It will lead to a balanced situation.However,this kind of equilibrium tends to reduce the overall revenue of customers,so it is necessary to find the social optimal strategy from a global perspective,which is the focus of our attention.This paper mainly studies the strategic behavior of customers in two types of retrial queuing systems.Model 1 considers a constant retrial queue with reserved time and vacation.Firstly,the conditions for the steady state of the system are analyzed.By introducing an appropriate revenue structure,the equilibrium strategy of customers is obtained under fully unobservable case,and the social optimal strategy is further discussed.Finally,two strategies are compared and numerical examples are given to illustrate the influence of the main parameters.Model 2 studies a constant retrial queue with balking and set-up time under almost unobservable case.Firstly,the steady-state solutions are obtained by using the generating function,and the individual equilibrium strategy is proposed by analyzing the customer's utility function.In addition,from the perspective of social managers and service providers,the maximization of social benefits and cost analysis are discussed,and the optimal arrival rates are derived,respectively.Finally,numerical examples are given by using the PSO algorithm,and the sensitivity of main parameters is analyzed.