Age-of-Information in Clocked Networks

We derive key features of the Age-of-Information distribution in a system whose activities are strictly limited to periodic instances on a global time grid. In particular, one agent periodically generates updates while the other agent periodically uses the most recently received of those updates. Likewise, transmission of those updates over a network can only occur periodically. All periods may differ. We derive results for two different models: a basic one in which the mathematical problems can be handled directly and an extended model which, among others, can also account for stochastic transmission failure, making the results applicable to instances with wireless communication. For both models, a suitable approximation for the expected Age-of-Information and an upper bound for its largest occurring value are developed. For the extended model (which is the more relevant one from a practical standpoint) we also present numerical results for the distribution of the approximation error for numerous parameter choices

Age of Information of a Server with Energy Requirements

We investigate a system with Poisson arrivals to two queues. One queue stores the status updates of the process of interest (or data packets) and the other handles the energy that is required to deliver the updates to the monitor. We consider that the energy is represented by packets of discrete unit. When an update ends service, it is sent to the energy queue and, if the energy queue has one packet, the update is delivered successfully and the energy packet disappears; however, in case the energy queue is empty, the update is lost. Both queues can handle, at most, one packet and the service time of updates is exponentially distributed. Using the Stochastic Hybrid System method, we characterize the average Age of Information of this system. Due to the difficulty of the derived expression, we also explore approximations of the average Age of Information of this systemJosu Doncel has received funding from the Department of Education of the Basque Government through the Consolidated Research Group MATHMODE (IT1294-19), from the Marie Sklodowska-Curie grant agreement No. 777778 and from from the Spanish Ministry of Science and Innovation with reference PID2019-108111RB-I00 (FEDER/AEI). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscrip

On the Age of Information of Processor Sharing Systems

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