  We consider a time-slotted status update system with an error-free preemptive
queue. The goal of the sampler-scheduler pair is to minimize the age of
information at the monitor by sampling and transmitting the freshly sampled
update packets to the monitor. The sampler-scheduler pair also has a choice to
preempt an old update packet from the server and transmit a new update packet
to the server. We formulate this problem as a Markov decision process (MDP) and
find the optimal sampling policy. We find a sufficient, and also separately a
necessary, condition for the always preemption policy to be an optimal policy.
We show that it is optimal for the sampler-scheduler pair to sample a new
packet immediately upon the reception of an update packet at the monitor. We
propose a double-threshold sampling policy which we show to be an optimal
policy under some assumptions on the queue statistic.
