Enforcing global serializability in such system, where different databases may use different types of concurrency control, is problematic.
Achieving global serializability effectively over different types of concurrency control has been open for several years.
Among them (with several publications each): Another common reason nowadays for Global serializability relaxation is the requirement of availability of internet products and services.
No distinction between global and local cycles exists for RCSR properties that are not RGCSR.
Typically RGCSR techniques eliminate local cycles, i.e., provide local serializability (which can be achieved effectively by regular, known concurrency control methods); however, obviously they do not eliminate all global cycles (which would achieve global serializability).