  A resource-constrained system monitors a source of information by requesting
a finite number of updates subject to random transmission delays. An a priori
fixed update request policy is shown to minimize a polynomial penalty function
of the age of information over arbitrary time horizons. Partial updates,
compressed updates with reduced transmission and information content, in the
presented model are shown to incur an age penalty independent of the
compression. Finite horizons are shown to have better performance in terms of
second order statistic relative to infinite horizons.
