On the Age of Information of Processor Sharing Systems

Abstract: 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.