Research On Equilibrium Strategies Of Retrial Queue With N-policy

The traditional queueing theory is based on the stochastic process,and the system is researched on the system such as queue length7 sojourn time,busy cycle,etc.The customer's strategic behavior is often ignored in the traditional queueing theory,the economic utility of the customer and the impacts it brings on the performance of system are seldom considered.Hence,there has been an upsurge of studying queueing theory from the perspective of economics.From the perspective of how to maximize his own benefit,the customer decide whether to enter the system based on a reward-cost structure function which we construct,unavoidably,each customer's behavior will be affected by the other customers and eventually reach a balance,which creates a equilibrium situation.We have done the following works in this article:Model 1 considers equilibrium strategies of the constant retrial queue with the N-policy,under the server's state and the queue length can be observed,we are concerned about the strategic behavior of arriving customers and obtain social welfare expressions.Moreover,we also study the customers' equilibrium balking threshold,and make sensitivity analysis of social opti-mal balking threshold and optimal social welfare with respect to N and the constant retrial rate respectively when other parameter values are given;Model 2 studies the strategic behavior and social optimization in a constant retrial queue with setup time and the N-policy.In this model,only the server's state can be observed.We give the ef-fective equilibrium arrival rates between the different server's states and the expression of social welfare by establishing the corresponding reward-cost structure.Finally,we solve the social optimation of four-dimensional variables through the Particle Swarm Optimization(PSO)algorithm and give the corresponding numerical examples.