  We consider a setting where multiple active sources send real-time updates
over a single-hop wireless broadcast network to a monitoring station. Our goal
is to design a scheduling policy that minimizes the time-average of general
non-decreasing cost functions of Age of Information. We use a Whittle index
based approach to find low complexity scheduling policies that have good
performance. We prove that for a system with two sources, having possibly
different cost functions and reliable channels, the Whittle index policy is
exactly optimal. We derive structural properties of an optimal policy, that
suggest that the performance of the Whittle index policy may be close to
optimal in general. These results might also be of independent interest in the
study of restless multi-armed bandit problems with similar underlying
structure. We further establish that minimizing monitoring error for linear
time-invariant systems and symmetric Markov chains is equivalent to minimizing
appropriately chosen monotone functions of Age of Information. Finally, we
provide simulations comparing the Whittle index policy with optimal scheduling
policies found using dynamic programming, which support our results.
