Analysis of the equilibrium strategies in the Geo/Geo/1 queue with   multiple working vacations
  This paper studies the equilibrium behavior of customers in the Geo/Geo/1 queueing system with multiple working vacations. The arriving customers decide whether to join or to balk the queueing systems based on the information of the queue length and the states of the server. In observable queues, partially observable queues and unobservable queues three cases we obtain the equilibrium balking strategies based on the reward-cost structure and socially optimal strategies for all customers. Furthermore, we present some numerical experiments to illustrate the effect of the information level on the equilibrium behavior and to compare the customers' equilibrium and socially optimal strategies. 
Yang Bixuan, Hou Zhenting, Wu Jinbiao, Liu Zaiming
math.PR