  Age of Information (AoI) has emerged as an important quality-of-service
measure for applications that prioritize delivery of the freshest information,
e.g., virtual or augmented reality over mobile devices and wireless sensor
networks used in the control of cyber-physical systems. We derive the Laplace
transform of the stationary AoI for the M/GI/1/2 system with a "dynamic"
service preemption and pushout policy depending on the existing service time of
the in-service message. Thus, our system generalizes both the static M/GI/1/2
queue-pushout system without service preemption and the M/GI/1/1 bufferless
system with service preemption - two systems considered to provide very good
AoI performance. Based on our analysis, for a service-time distribution that is
a mixture of deterministic and exponential, we numerically show that the
dynamic policy has lower mean AoI than that of these two static policies and
also that of the well studied M/GI/1/1 blocking system.
