  Age of Information (AoI) and Peak AoI (PAoI) and their analytical models have
recently drawn substantial amount of attention in information theory and
wireless communications disciplines, in the context of qualitative assessment
of information freshness in status update systems. We take a queueing-theoretic
approach and study a probabilistically preemptive bufferless $M/PH/1/1$
queueing system with arrivals stemming from $N$ separate information sources,
with the aim of modeling a generic status update system. In this model, a new
information packet arrival from source $m$ is allowed to preempt a packet from
source $n$ in service, with a probability depending on $n$ and $m$. To make the
model even more general than the existing ones, for each of the information
sources, we assume a distinct PH-type service time distribution and a distinct
packet error probability. Subsequently, we obtain the exact distributions of
the AoI and PAoI for each of the information sources using matrix-analytical
algorithms and in particular the theory of Markov fluid queues and sample path
arguments. This is in contrast with existing methods that rely on Stochastic
Hybrid Systems (SHS) which obtain only the average values and in less general
settings. Numerical examples are provided to validate the proposed approach as
well as to give engineering insight on the impact of preemption probabilities
on certain AoI and PAoI performance figures.
