Abstract Considering the power consumption and delay performance, we propose a clearing queueing system with N-policy and stochastic restarting scheme. At the service completion epoch, the server switches to the dormant state to save energy if there are no customers waiting for services, otherwise initiates a new clearing service. After a dormant period, the server will be activated if there are at least N waiting customers, and be activated stochastically with less than N waiting customers. We derive the stationary distribution of system states with the closed form and an effective algorithm is designed to obtain the distribution of the sojourn time. In addition, a reward-cost structure is introduced in the queueing system. We analyze customers’ equilibrium strategic behaviours based on the optimistic value and provide a comparison between the criteria of using average and optimistic value by numerical examples. Finally, we discuss the social optimization problems and present some numerical experiences to illustrate impacts of system parameters on the socially optimal strategies and social optimal welfare.

中文翻译：

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具有N策略和随机重启方案的清算排队系统中的策略行为和社会优化

摘要 考虑到功耗和延迟性能，我们提出了一种具有N策略和随机重启方案的清除排队系统。在服务完成时期，如果没有客户等待服务，则服务器切换到休眠状态以节省能源，否则启动新的清算服务。休眠一段时间后，如果至少有 N 个等待客户，则服务器将被激活，并在等待客户少于 N 个时随机激活。我们以封闭形式导出系统状态的平稳分布，并设计了一种有效的算法来获得逗留时间的分布。此外，在排队系统中引入了奖励成本结构。我们基于乐观价值分析了客户的均衡战略行为，并通过数值例子提供了使用平均值和乐观价值的标准之间的比较。最后，我们讨论了社会优化问题，并提出了一些数值经验来说明系统参数对社会最优策略和社会最优福利的影响。