  In this work, we study age-optimal scheduling with stability constraints in a
multiple access channel with two heterogeneous source nodes transmitting to a
common destination. The first node is connected to a power grid and it has
randomly arriving data packets. Another energy harvesting (EH) sensor monitors
a stochastic process and sends status updates to the destination. We formulate
an optimization problem that aims at minimizing the average age of information
(AoI) of the EH node subject to the queue stability condition of the
grid-connected node. First, we consider a Probabilistic Random Access (PRA)
policy where both nodes make independent transmission decisions based on some
fixed probability distributions. We show that with this policy, the average AoI
is equal to the average peak AoI, if the EH node only sends freshly generated
samples. In addition, we derive the optimal solution in closed form, which
reveals some interesting properties of the considered system. Furthermore, we
consider a Drift-Plus-Penalty (DPP) policy and develop AoI-optimal and
peak-AoI-optimal scheduling algorithms using the Lyapunov optimization theory.
Simulation results show that the DPP policy outperforms the PRA policy in
various scenarios, especially when the destination node has low multi-packet
reception capabilities.
