In this paper, we examine the Age of Information (AoI) of a source sending status updates to a monitor through a queue operating under the Processor Sharing (PS) discipline. In the PS queueing discipline, all the updates are served simultaneously and, therefore, none of of the jobs wait in the queue to get service. While AoI has been well studied for various queuing models and policies, less attention has been given so far to the PS discipline. We first consider the M/M/1/2 queue with and without preemption and provide closed-form expressions for the average AoI in this case. We overcome the challenges of deriving the AoI expression by employing the Stochastic Hybrid Systems (SHS) tool. We then extend the analysis to the M/M/1 queue with one and two sources and provide numerical results for these cases. Our results show that PS can outperform the M/M/1/1* queue in some cases.

翻译：本文研究通过处理器共享（Processor Sharing, PS）队列向监控器发送状态更新的源节点的信息年龄（Age of Information, AoI）。在PS队列调度策略中，所有更新同时被服务，因此没有任务需要排队等待服务。尽管AoI已在多种排队模型和策略中得到充分研究，但目前对PS策略的关注仍然相对不足。我们首先考虑具有和没有抢占机制的M/M/1/2队列，并给出该情况下平均AoI的闭式表达式。通过采用随机混合系统（Stochastic Hybrid Systems, SHS）工具，我们克服了推导AoI表达式面临的挑战。随后将分析扩展到具有单源和双源的M/M/1队列，并给出这些情况下的数值结果。结果表明，在某些场景下PS可优于M/M/1/1*队列。