  In this work, we study how to optimally manage the freshness of information
updates sent from a source node to a destination via a channel. A proper metric
for data freshness at the destination is the age-of-information, or simply age,
which is defined as how old the freshest received update is since the moment
that this update was generated at the source node (e.g., a sensor). A
reasonable update policy is the zero-wait policy, i.e., the source node submits
a fresh update once the previous update is delivered and the channel becomes
free, which achieves the maximum throughput and the minimum delay.
Surprisingly, this zero-wait policy does not always minimize the age. This
counter-intuitive phenomenon motivates us to study how to optimally control
information updates to keep the data fresh and to understand when the zero-wait
policy is optimal. We introduce a general age penalty function to characterize
the level of dissatisfaction on data staleness and formulate the average age
penalty minimization problem as a constrained semi-Markov decision problem
(SMDP) with an uncountable state space. We develop efficient algorithms to find
the optimal update policy among all causal policies, and establish sufficient
and necessary conditions for the optimality of the zero-wait policy. Our
investigation shows that the zero-wait policy is far from the optimum if (i)
the age penalty function grows quickly with respect to the age, (ii) the packet
transmission times over the channel are positively correlated over time, or
(iii) the packet transmission times are highly random (e.g., following a
heavy-tail distribution).
