In this paper, equilibrium strategies and optimal balking strategies of customers in a constant retrial queue with multiple vacations and the N-policy under two information levels, respectively, are investigated. We assume that there is no waiting area in front of the server and an arriving customer is served immediately if the server is idle; otherwise (the server is either busy or on a vacation) it has to leave the system to join a virtual retrial orbit waiting for retrials according to the FCFS rules. After a service completion, if the system is not empty, the server becomes idle, available for serving the next customer, either a new arrival or a retried customer from the virtual retrial orbit; otherwise (if the system is empty), the server starts a vacation. Upon the completion of a vacation, the server is reactivated only if it finds at least N customers in the virtual orbit; otherwise, the server continues another vacation. We study this model at two levels of information, respectively. For each level of information, we obtain both equilibrium and optimal balking strategies of customers, and make corresponding numerical comparisons. Through Particle Swarm Optimization (PSO) algorithm, we explore the impact of parameters on the equilibrium and social optimal thresholds, and obtain the trend in changes, as a function of system parameters, for the optimal social welfare, which provides guiding significance for social planners. Finally, by comparing the social welfare under two information levels, we find that whether the system information should be disclosed to customers depends on how to maintain the growth of social welfare.

本文研究了具有多个假期的恒定重试队列和N- 分别调查了两个信息级别下的政策。我们假设服务器前没有等候区，如果服务器空闲，则立即为到达的客户提供服务；否则（服务器要么忙要么在休假）它必须离开系统加入虚拟重试轨道，根据 FCFS 规则等待重试。服务完成后，如果系统不为空，则服务器空闲，可用于服务下一个客户，新客户或来自虚拟重试轨道的重试客户；否则（如果系统为空），服务器开始休假。假期结束后，服务器仅在找到至少N 个时重新激活虚拟轨道上的客户；否则，服务器将继续另一个假期。我们分别在两个信息层次上研究这个模型。对于每一层信息，我们都得到了客户的均衡策略和最优阻挠策略，并进行了相应的数值比较。通过粒子群优化（PSO）算法，我们探索了参数对均衡和社会最优阈值的影响，并获得了作为系统参数的函数的变化趋势，以获得最优的社会福利，为社会规划者提供指导意义. 最后，通过比较两个信息层次下的社会福利，我们发现系统信息是否应该向客户公开，取决于如何保持社会福利的增长。