  Future real-time applications like smart cities will use complex Machine
Learning (ML) models for a variety of tasks. Timely status information is
required for these applications to be reliable. Offloading computation to a
mobile edge cloud (MEC) can reduce the completion time of these tasks. However,
using the MEC may come at a cost such as related to use of a cloud service or
privacy. In this paper, we consider a source that generates time-stamped status
updates for delivery to a monitor after processing by the mobile device or MEC.
We study how a scheduler must forward these updates to achieve timely updates
at the monitor but also limit MEC usage. We measure timeliness at the monitor
using the age of information (AoI) metric. We formulate this problem as an
infinite horizon Markov decision process (MDP) with an average cost criterion.
We prove that an optimal scheduling policy has an age-threshold structure that
depends on how long an update has been in service.
