I was recently reading about random multiple access methods without time synchronisation (of the pure Aloha type). In this paper it is stated that,
The need for transmitter synchronization is a major drawback for large networks as the signaling overhead scales up with the number of transmitters independently from their traffic activity factor.
I understand that oscillators tend to drift in time and present instabilities depending on the technology, operating conditions, etc., and therefore a reference signal must be given by the central node with a periodicity that depends on the desired accuracy and the transmitter's clock drift.
I would like to know why there is also a dependency on the network size.
EDIT: The only scenario I can think of where signalling scales up with the network size, is a distributed network (but in that context, we usually talk about logical clocks and not about hardware clocks/oscillators). Note also that the network described in the paper has a star topology, so a periodic broadcast message from the central node would do, independently on the number of users in the network.