Evaluating Peak Age-of-Information via Stochastic Hybrid Systems

In this paper, we derive a general formula for the average peak age-of-information (PAoI) in the updating systems that can be modeled by a stochastic hybrid system (SHS) without fake updates. In such systems, updates in the age-of-information (AoI) process are equivalent to a set of transitions in the SHS. In our derivation, we first introduce the stochastic peak function whose limiting average is related to the average PAoI. Next, we utilize a new SHS that includes the stochastic peak function to find the average PAoI. As a case study, we investigate the average PAoI of a preemptive tandem network, where a newly arrived packet at a node replaces the old packet (if it exists).