  Cascade stability of load balancing is critical for ensuring high efficiency
service delivery and preventing undesirable handovers. In energy efficient
networks that employ diverse sleep mode operations, handing over traffic to
neighbouring cells' expanded coverage must be done with minimal side effects.
Current research is largely concerned with designing distributed and
centralized efficient load balancing policies that are locally stable. There is
a major research gap in identifying large-scale cascade stability for networks
with heterogeneous load balancing policies arising from diverse plug-and-play
sleep mode policies in ORAN, which will cause heterogeneity in the network
stability behaviour.
  Here, we investigate whether cells arbitrarily connected for load balancing
and having an arbitrary number undergoing sleep mode can: (i) synchronize to a
desirable load-balancing state, and (ii) maintain stability. For the first
time, we establish the criterion for stability and prove its validity for any
general load dynamics and random network topology. Whilst its general form
allows all load balancing and sleep mode dynamics to be incorporated, we
propose an ORAN architecture where the network service management and
orchestration (SMO) must monitor new load balancing policies to ensure overall
network cascade stability.
