  While the notion of age of information (AoI) has recently been proposed for
analyzing ultra-reliable low-latency communications (URLLC), most of the
existing works have focused on the average AoI measure. Designing a wireless
network based on average AoI will fail to characterize the performance of URLLC
systems, as it cannot account for extreme AoI events, occurring with very low
probabilities. In contrast, this paper goes beyond the average AoI to improve
URLLC in a vehicular communication network by characterizing and controlling
the AoI tail distribution. In particular, the transmission power minimization
problem is studied under stringent URLLC constraints in terms of probabilistic
AoI for both deterministic and Markovian traffic arrivals. Accordingly, an
efficient novel mapping between AoI and queue-related distributions is
proposed. Subsequently, extreme value theory (EVT) and Lyapunov optimization
techniques are adopted to formulate and solve the problem considering both long
and short packets transmissions. Simulation results show over a two-fold
improvement, in shortening the AoI distribution tail, versus a baseline that
models the maximum queue length distribution, in addition to a tradeoff between
arrival rate and AoI.
