  In this paper, we study joint batching and (task) scheduling to maximise the
throughput (i.e., the number of completed tasks) under the practical
assumptions of heterogeneous task arrivals and deadlines. The design aims to
optimise the number of batches, their starting time instants, and the
task-batch association that determines batch sizes. The joint optimisation
problem is complex due to multiple coupled variables as mentioned and numerous
constraints including heterogeneous tasks arrivals and deadlines, the causality
requirements on multi-task execution, and limited radio resources. Underpinning
the problem is a basic tradeoff between the size of batch and waiting time for
tasks in the batch to be uploaded and executed. Our approach of solving the
formulated mixed-integer problem is to transform it into a convex problem via
integer relaxation method and $\ell_0$-norm approximation. This results in an
efficient alternating optimization algorithm for finding a close-to-optimal
solution. In addition, we also design the optimal algorithm from leveraging
spectrum holes, which are caused by fixed bandwidth allocation to devices and
their asynchronized multi-batch task execution, to admit unscheduled tasks so
as to further enhance throughput. Simulation results demonstrate that the
proposed framework of joint batching and resource allocation can substantially
enhance the throughput of multiuser edge-AI as opposed to a number of simpler
benchmarking schemes, e.g., equal-bandwidth allocation, greedy batching and
single-batch execution.
