  This letter provides query-age-optimal joint sampling and transmission
scheduling policies for a heterogeneous status update system, consisting of a
stochastic arrival and a generate-at-will source, with an unreliable channel.
Our main goal is to minimize the average query age of information (QAoI)
subject to average sampling, average transmission, and per-slot transmission
constraints. To this end, an optimization problem is formulated and solved by
casting it into a linear program. We also provide a low-complexity near-optimal
policy using the notion of weakly-coupled constrained Markov decision
processes. The numerical results show up to 32% performance improvement by the
proposed policies compared with a benchmark policy.
