  For ultra-reliable, low-latency communications (URLLC) applications such as
mission-critical industrial control and extended reality (XR), it is important
to ensure the communication quality of individual packets.
  Prior studies have considered Probabilistic Per-packet Real-time
Communications (PPRC) guarantees for single-cell, single-channel networks, but
they have not considered real-world complexities such as inter-cell
interference in large-scale networks with multiple communication channels and
heterogeneous real-time requirements. To fill the gap, we propose a real-time
scheduling algorithm based on \emph{local-deadline-partition (LDP)}, and the
LDP algorithm ensures PPRC guarantee for large-scale, multi-channel networks
with heterogeneous real-time constraints. We also address the associated
challenge of schedulability test. In particular, we propose the concept of
\emph{feasible set}, identify a closed-form sufficient condition for the
schedulability of PPRC traffic, and then propose an efficient distributed
algorithm for the schedulability test.
  We numerically study the properties of the LDP algorithm and observe that it
significantly improves the network capacity of URLLC, for instance, by a factor
of 5-20 as compared with a typical method. Furthermore, the PPRC traffic
supportable by the LDP algorithm is significantly higher than that of
state-of-the-art comparison schemes. This demonstrates the potential of
fine-grained scheduling algorithms for URLLC wireless systems regarding
interference scenarios.
