  Information freshness and low latency communication is important to many
emerging applications. While Age of Information (AoI) serves as a metric of
information freshness, packet delay is a traditional metric of communication
latency. We prove that there is a natural tradeoff between the AoI and packet
delay. We consider a single server system, in which at most one update packet
can be serviced at a time. The system designer controls the order in which the
packets get serviced and the service time distribution, with a given service
rate. We analyze two tradeoff problems that minimize packet delay and the
variance in packet delay, respectively, subject to an average age constraint.
We prove a strong age-delay and age-delay variance tradeoff, wherein, as the
average age approaches its minimum, the delay and its variance approach
infinity. We show that the service time distribution that mininizes average
age, must necessarily have an unbounded-second moment.
